Hillary – Page 32 – Math in Focus Answer Key

Math in Focus Kindergarten Chapter 14 Answer Key Number Facts

September 24, 2024September 23, 2024 by Hillary

Go through the Math in Focus Grade K Workbook Answer Key Chapter 14 Number Facts to finish your assignments.

Math in Focus Kindergarten Chapter 14 Answer Key Number Facts

Lesson 1 Number Facts to 10

Count, write, and circle.

$Math in Focus Kindergarten Chapter 14 Answer Key 1$

Question 1.
$Math in Focus Kindergarten Chapter 14 Answer Key 2$
How many in all?
2
4
6
Answer:
Count the blue bottles and yellow bottles.
The total number of blue bottles=4
The total number of yellow bottles=2
The total number of blue and yellow bottles combine=4+2=6
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q1$

Question 2.
$Math in Focus Kindergarten Chapter 14 Answer Key 3$
How many in all?
3
6
7
Answer: 6
Count the blue bottles and yellow bottles.
The total number of blue bottles=5
The total number of yellow bottles=1
The total number of blue and yellow bottles combine=5+1=6
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q2$

Question 3.
$Math in Focus Kindergarten Chapter 14 Answer Key 4$
How many in all?
8
9
10
Answer: 8
Count the blue bottles and yellow bottles.
The total number of blue bottles=3
The total number of yellow bottles=5
The total number of blue and yellow bottles combine=3+5=8
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q3$

Question 4.
$Math in Focus Kindergarten Chapter 14 Answer Key 5$
How many in all?
7
8
10
Answer: 10
Count the blue bottles and yellow bottles.
The total number of blue bottles=2
The total number of yellow bottles=8
The total number of blue and yellow bottles combine=2+8=10

Question 5.
$Math in Focus Kindergarten Chapter 14 Answer Key 6$
How many in all?
10
11
12
Answer:
Count the blue bottles and yellow bottles.
The total number of blue bottles=7
The total number of yellow bottles=3
The total number of blue and yellow bottles combine=7+3=10
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q5$

Color, count and write. Write the number sentence.

$Math in Focus Kindergarten Chapter 14 Answer Key 7$

Question 1.
$Math in Focus Kindergarten Chapter 14 Answer Key 8$
5 is _________ and ________.
Answer:
The sum of two positive integers 3 and 2 is 5
3+2=5
3 and 2 make 5
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=5
We need to colour them red and green.
So we can colour 3 red boxes and 2 green boxes.
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q18$

Question 2.
$Math in Focus Kindergarten Chapter 14 Answer Key 9$
5 is _________ and ________.
Answer:
The sum of two positive integers 4 and 1 is 5
4+1=5
4 and 1 make 5
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=5
We need to colour them red and green.
So we can colour 4 red boxes and 1 green box.
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q19$

Question 3
$Math in Focus Kindergarten Chapter 14 Answer Key 10$
7 is _________ and ________.
Answer:
The sum of two positive integers 3 and 4 is 7
3+4=7
3 and 4 make 7
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=7
We need to colour them red and green.
So we can colour 3 red boxes and 4 green boxes.
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q20$

Question 4.
$Math in Focus Kindergarten Chapter 14 Answer Key 11$
9 is _________ and ________.
Answer:
The sum of two positive integers 4 and 5 is 9
4+5=9
4 and 5 make 9
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=9
We need to colour them red and green.
So we can colour 4 red boxes and 5 green boxes.
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q21$

Question 5.
$Math in Focus Kindergarten Chapter 14 Answer Key 12$
9 is _________ and ________.
Answer:
The sum of two positive integers 8 and 1 is 9
8+1=9
8 and 1 make 9
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=9
We need to colour them red and green.
So we can colour 8 red boxes and 1 green box.
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q22$

Lesson 2 Combining Sets

Count and write.

$Math in Focus Kindergarten Chapter 14 Answer Key 13$

Question 1.
$Math in Focus Kindergarten Chapter 14 Answer Key 14$
Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of apples=9
We need to find out the number of more apples needed to make 10=X
X=10-9
X=1
Therefore, 1 more apple is needed to make 10.

Question 2.
$Math in Focus Kindergarten Chapter 14 Answer Key 15$
Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of glasses=5+3=8
We need to find out the number of more glasses needed to make 10=X
X=10-8
X=2
Therefore, 2 more glasses are needed to make 10.

Question 3.
$Math in Focus Kindergarten Chapter 14 Answer Key 16$
Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of pizzas=2+1=3
We need to find out the number of more pizzas needed to make 10=X
X=10-3
X=7
Therefore, 7 more pizzas are needed to make 10.

Question 4.
$Math in Focus Kindergarten Chapter 14 Answer Key 17$
Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of sandwiches=6+3=9
We need to find out the number of more sandwiches needed to make 10=X
X=10-9
X=1
Therefore, 1 more sandwich is needed to make 10.

Question 5.
$Math in Focus Kindergarten Chapter 14 Answer Key 18$
Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of toys=3+2=5
We need to find out the number of more toys needed to make 10=X
X=10-5
X=5
Therefore, 5 more toys are needed to make 10.

Lesson 3 Composing and Decomposing Numbers to 20

Count and write. Write the number sentence.

Question 1.
$Math in Focus Kindergarten Chapter 14 Answer Key 19$
Answer:
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q12$
5+2=7
The sum of two positive integers 5 and 2 is 7.

Question 2.
$Math in Focus Kindergarten Chapter 14 Answer Key 20$
_________ and __________ make ___________.
Answer:
The sum of two positive integers 0 and 5 is 5
0+5=5
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q13$

Question 3.
$Math in Focus Kindergarten Chapter 14 Answer Key 21$
_________ and __________ make ___________.
Answer:
The sum of two positive integers 5 and 5 is 10
5 and 5 make 10.
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q14$

Question 4.
$Math in Focus Kindergarten Chapter 14 Answer Key 22$
_________ and __________ make ___________.
Answer:
The sum of two positive integers 10 and 2 is 12
10+2=12
10 and 2 make 12.
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q15$

Question 5.
$Math in Focus Kindergarten Chapter 14 Answer Key 23$
_________ and __________ make ___________.
Answer:
The sum of two positive integers 10 and 5 is 15
10+5=15
10 and 5 make 15
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q16$

Question 6.
$Math in Focus Kindergarten Chapter 14 Answer Key 24$
_________ and __________ make ___________.
Answer:
The sum of two positive integers 10 and 7 is 17
10+7=17
10 and 7 make 17
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q17$

Draw $Math in Focus Kindergarten Chapter 14 Answer Key 25$ . Write the number sentence.

Question 1.
$Math in Focus Kindergarten Chapter 14 Answer Key 26$
Answer:
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q7$
5+2=7
So we can write in sentences,
adding 5 and 2 we get 7.

Question 2.
$Math in Focus Kindergarten Chapter 14 Answer Key 27$
__________ is __________ and ___________.
Answer: 9 is 5 and 4
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q8$
5+4=9
And some other ways we can write 9 is:
4+5=9
6+3=9
7+2=9
8+1=9
So we can write in sentences,
by adding above all we get 9.

Question 3.
$Math in Focus Kindergarten Chapter 14 Answer Key 28$
__________ is __________ and ___________.
Answer:
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q9$
5 is 4 and 1
and there are some other ways we can write 5:
2+3=5
3+2=5
4+1=5
So we can write in sentences,
by adding above all we get 5.

Question 4.
$Math in Focus Kindergarten Chapter 14 Answer Key 29$
__________ is __________ and ___________.
Answer:
16 is 10 and 6
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q10$
and there are some other ways we can write 16:
10+6=16
8+8=16
15+1=16
14+2=16
13+3=16
12+4=16
11+5=16
9+7=16
So we can write in sentences,
by adding above all we get 16.

Question 5.
$Math in Focus Kindergarten Chapter 14 Answer Key 30$
__________ is __________ and ___________.
Answer:
14 is 10 and 4
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q11$
and there are some other ways we can write 14:
2+12=14
13+1=14
11+3=14
10+4=14
9+5=14
8+6=14
7+7=14
6+8=14
5+9=14
So we can write in sentences,
by adding above all we get 14.

Lesson 4 Counting On

Count and write.

$Math in Focus Kindergarten Chapter 14 Answer Key 31$

Question 1.
$Math in Focus Kindergarten Chapter 14 Answer Key 32$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of honey bees = 6
We need to find out the number of more honey bees to make 15=X
X=15-6
X=9
Therefore, 9 more honey bees are needed to make 15.

Question 2.
$Math in Focus Kindergarten Chapter 14 Answer Key 33$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of ants = 11
We need to find out the number of more ants to make 15=X
X=15-11
X=4
Therefore, 4 more ants are needed to make 15.

Question 3.
$Math in Focus Kindergarten Chapter 14 Answer Key 34$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of snails = 12
We need to find out the number of more snails to make 15=X
X=15-12
X=3
Therefore, 3 more snails are needed to make 15.

Question 4.
$Math in Focus Kindergarten Chapter 14 Answer Key 35$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of flies = 9
We need to find out the number of more flies to make 15=X
X=15-9
X=6
Therefore, 6 more flies are needed to make 15.

Question 5.
$Math in Focus Kindergarten Chapter 14 Answer Key 36$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of caterpillars = 5
We need to find out the number of more caterpillars to make 15=X
X=15-5
X=10
Therefore, 10 more caterpillars are needed to make 15.

Count and write.

$Math in Focus Kindergarten Chapter 14 Answer Key 37$

Question 1.
$Math in Focus Kindergarten Chapter 14 Answer Key 38$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of flies is 8
$Math in Focus Kindergarten Chapter 14 Answer Key Number Facts q6$
The number of flies is needed to make 15 is ‘X’.
X=15-8
X=7
Therefore, 7 more are needed to make 15.

Question 2.
$Math in Focus Kindergarten Chapter 14 Answer Key 39$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of flies=6
The number of flies is needed to make 15 is ‘X’.
X=15-6
X=9
Therefore, 9 more are needed to make 15.

Question 3.
$Math in Focus Kindergarten Chapter 14 Answer Key 40$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of leaves=10
The number of leaves is needed to make 15 is ‘X’.
X=15-10
X=5
Therefore, 5 more are needed to make 15.

Question 4.
$Math in Focus Kindergarten Chapter 14 Answer Key 41$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of snails=5
The number of snails is needed to make 15 is ‘X’.
X=15-5
X=10
Therefore, 10 more are needed to make 15.

Question 5.
$Math in Focus Kindergarten Chapter 14 Answer Key 42$
Count how many. ____________
How many more to make 15? __________
Answer:
The number of ants=13
The number of ants is needed to make 15 is ‘X’.
X=15-13
X=2
Therefore, 2 more are needed to make 15.

Math in Focus Kindergarten Chapter 11 Answer Key Calendar Patterns

September 24, 2024September 23, 2024 by Hillary

Go through the Math in Focus Grade K Workbook Answer Key Chapter 11 Calendar Patterns to finish your assignments.

Math in Focus Kindergarten Chapter 11 Answer Key Calendar Patterns

Lesson 1 Days of the Week

What day is it today? Color green. What day was it yesterday? Color blue. What day will it be tomorrow? Color yellow.

$Math in Focus Kindergarten Chapter 11 Answer Key 1$
Answer:
$Math in Focus Kindergarten Chapter 11 Answer Key Calendar Patterns q1$
Explanation:
There are 7 days a week. They are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday
Today is a Monday so I coloured green.
Yesterday was Sunday so I coloured blue.
Tomorrow is a Tuesday so I coloured yellow.

Read and circle.

$Math in Focus Kindergarten Chapter 11 Answer Key 2$
Answer:
Explanation:
There are 7 days a week. They are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.
Saturday after Sunday.
Monday before Sunday.
$Math in Focus Kindergarten Chapter 11 Answer Key Calendar Patterns q2$

Lesson 2 Months of the Year

Make an X on the month before August. Circle the month after February. Color the month between October and December.

$Math in Focus Kindergarten Chapter 11 Answer Key 3$
Answer:
There are 12 months in a year. They are January, February, March, April, May, June, July, August, September, October, November, December.
– The month before August is July.
– The month after February is March.
– The month between October and December is November.
$Math in Focus Kindergarten Chapter 11 Answer Key Calendar Patterns q3$

Math in Focus Kindergarten Chapter 6 Answer Key Numbers 0 to 20

September 24, 2024September 23, 2024 by Hillary

Go through the Math in Focus Grade K Workbook Answer Key Chapter 6 Numbers 0 to 20 to finish your assignments.

Math in Focus Kindergarten Chapter 6 Answer Key Numbers 0 to 20

Lesson 1 All About 10

Sing.

$Math in Focus Kindergarten Chapter 6 Answer Key 1$
$Math in Focus Kindergarten Chapter 6 Answer Key 2$
Answer:

Count and write.

$Math in Focus Kindergarten Chapter 6 Answer Key 3$
Answer:

Explanation:
There are 2 giraffe
10 sheep and
4 cocks
$Math in Focus Kindergarten Chapter 6 Answer Key 4$
Answer:

Explanation:
There are 9 cherries
3 cows
5 ducks

Count and write.

$Math in Focus Kindergarten Chapter 6 Answer Key 5$
Answer:

Explanation:
Counted the fingers which are open

Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 6 Answer Key 6$
Answer:

Explanation:
Counted the blocks and Written the number
There are 10 blocks

Question 2.
$Math in Focus Kindergarten Chapter 6 Answer Key 7$
Answer:

Explanation:
Counted the blocks and Written the number
There are 9 blocks

Question 3.
$Math in Focus Kindergarten Chapter 6 Answer Key 8$
Answer:

Explanation:
Counted the blocks and Written the number
There are 8 blocks

Question 4.
$Math in Focus Kindergarten Chapter 6 Answer Key 9$
Answer:

Explanation:
Counted the blocks and Written the number
There are 10 blocks

Question 5.
$Math in Focus Kindergarten Chapter 6 Answer Key 10$
Answer:

Explanation:
Counted the blocks and Written the number
There are 9 blocks

Question 6.
$Math in Focus Kindergarten Chapter 6 Answer Key 11$
Answer:

Explanation:
Counted the blocks and Written the number
There are 10 blocks

Lesson 2 Numbers 10 to 12

Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 6 Answer Key 12$
Answer:
Explanation:
counted the flowers and written the number
there are 11 flowers

Question 2.
$Math in Focus Kindergarten Chapter 6 Answer Key 13$
Answer:
Explanation:
counted the bells and written the number
there are 12 bells

Question 3.
$Math in Focus Kindergarten Chapter 6 Answer Key 14$
Answer:
Explanation:
counted the bees and written the number
there are 12 bees

Question 4.
$Math in Focus Kindergarten Chapter 6 Answer Key 15$
Answer:
Explanation:
counted the eggs and written the number
there are 11 eggs

Question 5.
$Math in Focus Kindergarten Chapter 6 Answer Key 16$
Answer:
Explanation:
counted the bells and written the number
there are 12 bells

Question 6.
$Math in Focus Kindergarten Chapter 6 Answer Key 17$
Answer:
Explanation:
counted the glasses and written the number
there are 12 glasses

Question 7.
$Math in Focus Kindergarten Chapter 6 Answer Key 18$
Answer:
Explanation:
counted the ants and written the number
there are 11 ants

Question 8.
$Math in Focus Kindergarten Chapter 6 Answer Key 19$
Answer:
Explanation:
counted the leaves and written the number
there are 11 leaves

Read and draw $Math in Focus Kindergarten Chapter 6 Answer Key 20$ . Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 6 Answer Key 21$
How many in all? __________
Answer:

Explanation:
Counted and written the number
10 and 1 is 11
There are 11 in all

Question 2.
$Math in Focus Kindergarten Chapter 6 Answer Key 22$
How many in all? __________
Answer:

Explanation:
Counted and written the number
There are 10 in all

Question 3.
$Math in Focus Kindergarten Chapter 6 Answer Key 23$
How many in all? __________
Answer:

Explanation:
Counted and written the number
There are 8 in all

Question 4.
$Math in Focus Kindergarten Chapter 6 Answer Key 24$
How many in all? __________
Answer:

Explanation:
Counted and written the number
There are 12 in all

Lesson 3 Numbers 13 to 16

Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 6 Answer Key 25$
Answer:

Explanation:
Counted the cups and written the number
there are 11 cups

Question 2.
$Math in Focus Kindergarten Chapter 6 Answer Key 26$
Answer:

Explanation:
Counted the snails and written the number
there are 12 snails

Question 3.
$Math in Focus Kindergarten Chapter 6 Answer Key 27$
Answer:

Explanation:
Counted the ducks and written the number
there are 13 ducks

Question 4.
$Math in Focus Kindergarten Chapter 6 Answer Key 28$
Answer:

Explanation:
Counted the stars and written the number
there are 15 stars

Question 5.
$Math in Focus Kindergarten Chapter 6 Answer Key 29$
Answer:

Explanation:
Counted the balls and written the number
there are 15 balls

Question 6.
$Math in Focus Kindergarten Chapter 6 Answer Key 30$
Answer:

Explanation:
Counted the ants and written the number
there are 16 ants

Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 6 Answer Key 31$
Answer:

Explanation:
Counted the butterflies and written the number
there are 13 butterflies

Question 2.
$Math in Focus Kindergarten Chapter 6 Answer Key 32$
Answer:

Explanation:
Counted the hats and written the number
there are 16 hats

Question 3.
$Math in Focus Kindergarten Chapter 6 Answer Key 33$
Answer:

Explanation:
Counted the spoons and written the number
there are 15 spoons

Question 4.
$Math in Focus Kindergarten Chapter 6 Answer Key 34$
Answer:

Explanation:
Counted the pencils and written the number
there are 14 pencils

Lesson 4 Numbers 17 to 20

Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 6 Answer Key 35$
Answer:

Explanation:
Counted the sparrows and written the number
there are 15 sparrows

Question 2.
$Math in Focus Kindergarten Chapter 6 Answer Key 36$
Answer:

Explanation:
Counted the cherries and written the number
there are 16 cherries

Question 3.
$Math in Focus Kindergarten Chapter 6 Answer Key 37$
Answer:

Explanation:
Counted the glosses and written the number
there are 17 glosses

Question 4.
$Math in Focus Kindergarten Chapter 6 Answer Key 38$
Answer:

Explanation:
Counted the bricks and written the number
there are 18 bricks

Question 5.
$Math in Focus Kindergarten Chapter 6 Answer Key 39$
Answer:

Explanation:
Counted the oranges and written the number
there are 19 oranges

Question 6.
$Math in Focus Kindergarten Chapter 6 Answer Key 40$
Answer:

Explanation:
Counted the cups and written the number
there are 20 cups

Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 6 Answer Key 41$
Answer:

Explanation:
Counted the leaves and written the number
there are 20 leaves

Question 2.
$Math in Focus Kindergarten Chapter 6 Answer Key 42$
Answer:

Explanation:
Counted the carrots and written the number
there are 18 carrots

Question 3.
$Math in Focus Kindergarten Chapter 6 Answer Key 43$
Answer:

Explanation:
Counted the marbles and written the number
there are 19 marbles

Question 4.
$Math in Focus Kindergarten Chapter 6 Answer Key 44$
Answer:

Explanation:
Counted the mice and written the number
there are 17 mice

Read and draw $Math in Focus Kindergarten Chapter 6 Answer Key 45$ . Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 6 Answer Key 46$
How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 18 in all

Question 2.
$Math in Focus Kindergarten Chapter 6 Answer Key 47$
How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 16 in all

Question 3.
$Math in Focus Kindergarten Chapter 6 Answer Key 48$
How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 20 in all

Question 4.
$Math in Focus Kindergarten Chapter 6 Answer Key 49$
How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 17 in all

Read and draw $Math in Focus Kindergarten Chapter 6 Answer Key 45$ . Count and write.

Question 5.
$Math in Focus Kindergarten Chapter 6 Answer Key 50$
How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 15 in all

Question 6.
$Math in Focus Kindergarten Chapter 6 Answer Key 51$
How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 19 in all

Join the dots.

$Math in Focus Kindergarten Chapter 6 Answer Key 52$
Answer:

Explanation:
Joined the dots by tracing the numbers.

Lesson 5 Compare and Order

Count and write. Color the group with more.

$Math in Focus Kindergarten Chapter 6 Answer Key 53$
Answer:

Explanation:
Number of stars more than the hearts. So color the stars

Count and write. Color the group with fewer.
$Math in Focus Kindergarten Chapter 6 Answer Key 54$
Answer:

Explanation:
Number of glass fewer than the cups. So color the glasses

Draw the same number.
$Math in Focus Kindergarten Chapter 6 Answer Key 55$
Answer:

Explanation:
Counted the circles there are 8. So drawn the 8 circles.

Draw more.
$Math in Focus Kindergarten Chapter 6 Answer Key 56$
Answer:

Explanation:
Counted the circles there are 12. So drawn the 15 circles.
Since 15 is more than 12.

Draw fewer.
$Math in Focus Kindergarten Chapter 6 Answer Key 57$
Answer:

Explanation:
Counted the circles there are 20. So drawn the 12 circles.
Since 12 is fewer than 20.

Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10

September 24, 2024September 23, 2024 by Hillary

Go through the Math in Focus Grade K Workbook Answer Key Chapter 2 Numbers to 10 to finish your assignments.

Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10

Lesson 1 All about 6

Match.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 1$
Answer:

Explanation:
Counted the number of wheels and counted and matched the same number of wheels

Draw.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 2$
Answer:

Explanation:
counted and Drawn the number of dots

Trace.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 3$
Answer:

Explanation:
Traced the numbers from 1 to 6

Count and Write.

Question 1.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 4$
Answer:

Explanation:
Counted and written number of wheels
There are 6 wheels

Question 2.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 5$
Answer:

Explanation:
Counted and written number of cups
There are 6 cups

Question 3.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 6$
Answer:

Explanation:
Counted and written number of flags
There are 6 flags

Question 4.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 7$
Answer:

Explanation:
Counted and written number of oranges
There are 6 oranges

Question 5.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 8$
Answer:

Explanation:
Counted and written number of lemons
There are 6 lemons

Question 6.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 9$
Answer:

Explanation:
Counted and written number of onions
There are 6 onions

Lesson 2 All about 7

Sing.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 10$

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 11$

Circle the groups of seven bees.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 12$
Explanation:

Circled the group of seven bees

Match.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 13$
Explanation:

Counted the number of hives and matched with the same number of hives

Draw.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 14$
Explanation:

Counted and drawn the circles

Trace.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 15$
Explanation:

Traced the numbers from 6 and 7

Look and Say.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 16$

Count and Write.

Question 1.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 17$
Answer:
Explanation:
Counted and written number of hives
There are 7 hives

Question 2.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 18$
Answer:
Explanation:
Counted and written number of glasses
There are 7 glasses

Question 3.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 19$
Answer:
Explanation:
Counted and written number of cups
There are 7 cups

Question 4.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 20$
Answer:
Explanation:
Counted and written number of forks
There are 7 forks

Question 5.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 21$
Answer:
Explanation:
Counted and written number of bees
There are 7 bees

Question 6.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 22$
Answer:
Explanation:
Counted and written number of pencils
There are 7 pencils

Lesson 3 All about 8

Color.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 23$
Explanation:

According to the number colored the dots

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 24$
Explanation:

According to the number colored the dots

Draw.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 25$
Explanation:

According to the numbers drawn the apples

Match.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 26$
Explanation:
Counted the number of oranges and matched according to the same number of oranges

Draw.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 27$
Explanation:

Counted and drawn the same number of dots

Trace.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 28$
Explanation:

Written and traced the numbers from 1 to 4

Trace.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 29$

Explanation:

Written and traced the numbers from 5 to 8

Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 30$
Answer:

Explanation:
Counted and written number of balls
There are 8 balls

Question 2.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 31$
Answer:

Explanation:
Counted and written number of fishes
There are 8 fishes

Question 3.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 32$
Answer:

Explanation:
Counted and written number of bells
There are 8 bells

Question 4.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 33$
Answer:

Explanation:
Counted and written number of glasses
There are 8 glasses

Question 5.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 34$
Answer:

Explanation:
Counted and written number of spoons
There are 8 spoons

Question 6.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 35$
Answer:

Explanation:
Counted and written number of oranges
There are 8 oranges

Lesson 4 Numbers 0 to 9

Match.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 36$
Explanation:

Counted and matched the numbers from 1 to 9

Draw.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 37$
Explanation:

Drawn the same number of dots by counting the dots

Trace.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 38$

Explanation:

Traced the numbers from 1 to 5

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 39$
Explanation:

Traced the numbers from 6 to 9

Write the missing numbers.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 40$

Explanation:

Written the missing numbers

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 41$

Explanation:

Written the missing numbers

Count and write

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 42$
Explanation:

The second boy is holding only one glass

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 43$
Explanation:

In the above picture the first boy is catching 9 balloons
the second boy is catching 4 bottles and the third boy is catching 5 balls

Count and write.

Question 1.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 44$
Answer:

Explanation:
Counted and written number of Balls
There are 9 balls

Question 2.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 45$
Answer:

Explanation:
Counted and written number of birds
There are 9 birds

Question 3.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 46$
Answer:

Explanation:
Counted and written number of Eggs
There are 9 eggs

Question 4.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 47$
Answer:

Explanation:
Counted and written number of Carrots
There are 9 carrots

Question 5.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 48$
Answer:

Explanation:
Counted and written number of sticks
There are 9 sticks

Question 6.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 49$
Answer:

Explanation:
Counted and written number of Cheese
There are 9 cheese

Circle the group of 9 players.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 50$
Explanation:
In the above picture there are 10 boys circled 9 of them

Lesson 5 Pairing Sets with Numbers

Read, count, and circle.

Question 1.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 51$
Answer:
Explanation:
3 + 1 = 4
Circled the 4 birds

Question 2.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 52$
Answer:
Explanation:
4 – 1 = 3
Circled 3 fishes

Question 3.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 53$
Answer:
Explanation:
Circled the same number that is 2

Lesson 6 Pairing One-to-One

What is missing? Complete the set.

$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 54$
Explanation:
For cups saucer is missing
For bottles straw is missing
For cats tails are missing

Circle, Count, and write.

Question 1.
There is cheese for 6 mice.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 55$
How many mice will be hungry? ____
Answer:
3 will be hungry
Explanation:
There are 9 mice but only 6 cheese are there so 3 are missing

Question 2.
3 boys have coats.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 56$
How many boys will be cold? ____
Answer:
2 boys will be cold
Explanation:
There are 5 boys out of them 3 having coats
so 2 will be cold

Question 3.
There are 6 egg holders.
$Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10 57$
How many eggs are needed to fill all the egg holders? _____
Answer:
4 eggs are needed to fill all the egg holders
Explanation:
There are 6 egg holders out of them there are only 2 eggs
so 4 will be empty

Math in Focus Grade 6 Cumulative Review Chapters 4-7 Answer Key

September 24, 2024September 23, 2024 by Hillary

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Cumulative Review Chapters 4-7 to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Cumulative Review Chapters 4-7 Answer Key

Concepts and Skills

Write each ratio in simplest form. (Lesson 4.2)

Question 1.
12 : 28
Answer:
4 : 7
Explanation:
To find the simplest form of ratios we can use,
prime factor method or greatest common factor method.
12 : 28
common factor for both the numbers is 3
so, divided both sides with 3
12 : 28 = 4 : 7

Question 2.
32 : 18
Answer:
16 : 9
Explanation:
To find the simplest form of ratios we can use,
prime factor method or greatest common factor method.
32 : 18
common factor for both the numbers is 2
so, divided both sides with 2
32 : 18 = 16 : 9

Question 3.
36 : 81
Answer:
4 : 9
Explanation:
To find the simplest form of ratios we can use,
prime factor method or greatest common factor method.
36 : 81
common factor for both the numbers is 9
so, divided both sides with 9
36 : 81 = 4 : 9

Question 4.
64 : 40
Answer:
8 : 5
Explanation:
To find the simplest form of ratios we can use,
prime factor method or greatest common factor method.
64 : 40
common factor for both the numbers is 8
so, divided both sides with 8
64 : 40 = 8 : 5

Find the missing term in each pair of equivalent ratios. (Lesson 4.2)

Question 5.
35 : 25 = $Math in Focus Grade 6 Cumulative Review Chapters 4-7 Answer Key 1$ : 5
Answer:
Missing term is 7
Explanation:
product of extremes = product of means
a:b = c:d
ab = cd
ad = bc
a = 35, b = 25, c = x, d = 5
35 x 5 = 25x
25x = 175
x = 175 ÷ 25
x = 7

Question 6.
48 : 33 = 16 : $Math in Focus Grade 6 Cumulative Review Chapters 4-7 Answer Key 1$
Answer:
Missing term is 11
Explanation:
product of extremes = product of means
a:b = c:d
ab = cd
ad = bc
a = 48, b = 33, c = 16, d = x
48x = 33 x 16
48x = 528
x = 528 ÷ 48
x = 11

Question 7.
18 : $Math in Focus Grade 6 Cumulative Review Chapters 4-7 Answer Key 1$ = 9 : 12
Answer:
Missing term is 24
Explanation:
product of extremes = product of means
a:b = c:d
ab = cd
ad = bc
a = 18, b = x, c = 9, d = 12
18 x 12 = 9x
9x = 216
x = 216 ÷ 9
x = 24

Question 8.
$Math in Focus Grade 6 Cumulative Review Chapters 4-7 Answer Key 1$ : 24 = 21 : 14
Answer:
Missing term is 36
Explanation:
product of extremes = product of means
a:b = c:d
ab = cd
ad = bc
a = x, b = 24, c = 21, d = 14
14x = 24 x 21
14x = 504
x = 504 ÷ 14
x = 36

Express each percent as a fraction in simplest form. (Lesson 6.1)

Question 9.
58%
Answer:
= $\frac{29}{50}$
Explanation:
= $\frac{58}{100}$
= $\frac{29}{50}$

Question 10.
24$\frac{1}{3}$%
Answer:
2433.33
Explanation:
24 $\frac{1}{3}$ x 100
= $\frac{73}{3}$ x 100
= $\frac{73 x 100}{3}$
= $\frac{7300}{3}$
= 2433.33
Question 11.
9.4%
Answer:
$\frac{29}{50}$
Explanation:
9.4% = $\frac{9.4}{100}$
multiply the numerator and denominator with 10,
as numerator has decimal
= $\frac{94}{1000}$
Divided numerator and denominator with 2
= $\frac{47}{500}$

Express each percent as a decimal. (Lesson 6.1)

Question 12.
37%
Answer:
0.37
Explanation:
37% = $\frac{37}{100}$
= 0.37

Question 13.
67%
Answer:
0.67
Explanation:
67% = $\frac{67}{100}$
= 0.67

Question 14.
8.9%
Answer:
0.089
Explanation:
8.9% = $\frac{8.9}{100}$
= 0.089

Express each fraction as a percent. (Lesson 6.2)

Question 15.
$\frac{19}{20}$
Answer:
95%
Explanation:
$\frac{19}{20}$
= $\frac{19}{20}$ × 100%
= $\frac{1900}{20}$ %
= 95%

Question 16.
$\frac{23}{25}$
Answer:
92%
Explanation:
$\frac{23}{25}$
= $\frac{23}{25}$ × 100%
= $\frac{2300}{25}$ %
= 92%

Question 17.
$\frac{360}{400}$
Answer:
90%
Explanation:
$\frac{360}{400}$
= $\frac{360}{400}$ × 100%
= $\frac{36000}{400}$ %
= 90%

Express each decimal as a percent. (Lesson 6.2)

Question 18.
0.07
Answer:
7%
Explanation:
Express 0.04 as a percent.
Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.07 = $\frac{7}{100}$
= 0.07 x 100 = 7

Question 19.
0.62
Answer:
62%
Explanation:
Express 0.62 as a percent.
Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.62= $\frac{62}{100}$
= 0.62 x 100
= 62

Question 20.
0.8
Answer:
80%
Explanation:
Express 0.8 as a percent.
Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.8 = $\frac{8}{100}$
= 0.8 x 100
= 80

Find the quantity represented by each percent. (Lesson 6.3)

Question 21.
55% of 600 liters
Answer:
330 liters
Explanation:
55% of 600 liters
= $\frac{55}{100}$ × 600
= 330
66% of 740 is 330.

Question 22.
73% of $3,900
Answer:
$2,847
Explanation:
73% of $3,900
= $\frac{73}{100}$ × 3,900
= 2,847
73% of 740 is $2,847.

Write an algebraic expression for each of the following. (Lesson 7.1)

Question 23.
A number that is 7 more than 3 times x
Answer:
3x + 7
Explanation:
x + 7 is an algebraic expression in terms of x.
x and 7 are the terms of expression.
A number that is 7 more than 3 times x
3x + 7

Question 24.
The total cost, in cents, of 8 apples and 9 oranges if each apple costs 2y cents and each orange costs 3y cents
Answer:
43y cents
Explanation:
each apple costs 2y cents
each orange costs 3y cents
8 x 2y + 9 x 3y
= 16y + 27y
= 43y

Question 25.
The perimeter of a rectangle whose sides are of lengths (4z + 3) units and (3z + 5) units
Answer:
14z + 16 units
Explanation:
The perimeter of a rectangle = 2(Length + Breadth)
= 2 ( (4z + 3) + (3z + 5))
= 2 (4z + 3z + 3 + 5)
= 2 (7z + 8)
= 14z + 16

Evaluate each expression for the given value of the variable. (Lesson 7.2)

Question 26.
4(x + 5) – $\frac{2x}{3}$ when x = 6
Answer:
40
Explanation:
by substituting x value = 6 in the given algebraic equation
4(x + 5) – $\frac{2x}{3}$
= 4(6 + 5) – $\frac{2 x 6}{3}$
= (24 + 20) – $\frac{12}{3}$
= 44 – $\frac{12}{3}$
= (132 – 12) ÷ 3
= 120 ÷ 3
= 40

Question 27.
$\frac{6 y+7}{3}$ + $\frac{3 y+4}{4}$ when y = 8
Answer:
$\frac{152}{6}$ or 25.33
Explanation:
$\frac{6 y+7}{3}$ + $\frac{3 y+4}{4}$ when y = 8
= $\frac{6 x 8+7}{3}$ + $\frac{3 x 8+4}{4}$
= $\frac{48+7}{3}$ + $\frac{24+4}{4}$
= $\frac{55}{3}$ + $\frac{28}{4}$
= $\frac{304}{12}$
= $\frac{152}{6}$ or 25.33

Simplify each expression. (Lesson 7.3)

Question 28.
36a + 12 – 6a – 7
Answer:
30a + 5
Explanation:
36a + 12 – 6a – 7
= 36a – 6a + 12 – 7
= 30a + 5

Question 29.
21 + 34b – 8 – 5b + 8 + 23b
Answer:
Explanation:
21 + 34b – 8 – 5b + 8 + 23b
= 21 – 8 + 8 + 34b – 5b + 23b
= 21 + 52b

Expand each expression. (Lesson 7.4)

Question 30.
6(m + 4) + 3(m + 9)
Answer:
9m + 51
Explanation:
6(m + 4) + 3(m + 9)
= 6m + 24 + 3m + 27
= 9m + 51

Question 31.
8(n + 4) + 5(6 + n)
Answer:
13n + 62
Explanation:
8(n + 4) + 5(6 + n)
= 8n + 32 + 30 + 5n
= 13n + 62

Factor each expression. (Lesson 7.4)

Question 32.
6a – 42
Answer:
6(a – 7)
Explanation:
6a – 42
In the above expression 6 is a common factor
= 6(a – 7)

Question 33.
56 – 8b
Answer:
8(7 – b)
Explanation:
56 – 8b
In the above expression 8 is a common factor
= 8(7 – b)

Question 34.
23c + 37 – 5c + 8
Answer:
9(2c + 5)
Explanation:
23c + 37 – 5c + 8
= 23c – 5c + 37 + 8
= 18c + 45
= 9(2c + 5)

Question 35.
58 + 40d – 9 – 19d
Answer:
7(7 – 4d)
Explanation:
58 + 40d – 9 – 19d
= 58 – 9 + 40d – 19d
= 49 – 28d
= 7(7 – 4d)

Problem Solving

Solve. Show your work.

Question 36.
A factory produces 550 bottles of water in 25 minutes. How many bottles can it produce in 3 minutes? (Chapter 5)
Answer:
66 water bottles
Explanation:
A factory produces 550 bottles of water in 25 minutes.
Number of bottles can it produce in 3 minutes
= (550 x 3) ÷ 25
= 1650 ÷ 25 = 66

Question 37.
A machine can stamp 75 caps per minute. At this rate, how long will it take to stamp 3,000 caps? (Chapter 5)
Answer:
40 minutes
Explanation:
A machine can stamp 75 caps per minute
At this rate, how long will it take to stamp 3,000 caps
= 3000 ÷ 75
= 40 minutes

Question 38.
There were 65 students in the hall. 80% of them were girls. How many girls were in the hall? (Chapter 6)
Answer:
52 girls
Explanation:
There were 65 students in the hall.
80% of them were girls.
Number of girls in the hall
= 80% 0f 65
= $\frac{80}{100}$ X 65
= $\frac{5200}{100}$
= 52

Question 39.
Kenneth had $1,800. He spent 34% of it on a watch. How much did he pay for the watch? (Chapter 6)
Answer:
$612
Explanation:
Kenneth had $1,800.
He spent 34% of it on a watch.
Amount he paid for the watch
= 34% 0f 1800
= $\frac{34}{100}$ X 1800
= 34 X 18 = 612

Question 40.
28% of a number is 168. Find the number. (Chapter 6)
Answer:
number is 200
Explanation:
28% of a number is 168
28% of x = 168
$\frac{28}{100}$x = 168
$\frac{28x}{100}$ = 168
28x = 168 x 100
28x = 16800
x = 16800 ÷ 28
x = 600

Question 41.
140% of a number is 364. Find the number. (Chapter 6)
Answer:
number is 260
Explanation:
140% of a number is 364
140% of x = 364
$\frac{140}{100}$x = 364
$\frac{140x}{100}$ = 364
140x = 364 x 100
140x = 36400
x = 36400 ÷ 140
x = 260

Question 42.
Of the 90 students who sat for a test, 24 students passed. Find the ratio of the number of students who passed the test to the number of students who did not. Give your answer in simplest form. (Chapter 4)
Answer:
4 : 11
Explanation:
Of the 90 students who sat for a test, 24 students passed.
passed = 90 – 24 = 66
So, the ratio of the number of students who passed the test to the number of students who did not.
24 : 66 = 4 : 11
Question 43.
On Saturday, Aaron spent $108. On Sunday, he spent $54 more than what he spent on Saturday. Find the ratio of Aaron’s spending on Saturday to his spending on both Saturday and Sunday. Give your answer in simplest form. (Chapter 4)
Answer:
2 : 3
Explanation:
On Saturday, Aaron spent $108.
On Sunday, he spent $54 more than what he spent on Saturday.
$108 + $54 = $162
So, the ratio of Aaron’s spending on Saturday to his spending on both Saturday and Sunday.
108 : 162 = 2 : 3

Question 44.
A dalmatian weighs 72 pounds. A bullmastiff is 24 pounds heavier than the dalmatian. A bulldog is 12 pounds lighter than the bullmastiff. Find the ratio of the bulldog’s weight to the dalmatian’s weight. Give your answer in simplest form. (Chapter 4)
Answer:
7 : 6
Explanation:
A dalmatian weighs 72 pounds.
A bullmastiff is 24 pounds heavier than the dalmatian.
72 pounds + 24 pounds = 96 pounds
A bulldog is 12 pounds lighter than the bullmastiff.
96 pounds – 12 pounds = 84
The ratio of the bulldog’s weight to the dalmatian’s weight.
84 : 72 = 7 : 6

Question 45.
The ratio of the number of left-handers to the number of right-handers in a middle school is 6 : 15. If there are 120 left-handers, how many right-handers are there? (Chapter 4)
Answer:
300 right-handers
Explanation:
The ratio of the number of left-handers to the number of right-handers in a middle school is 6 : 15.
If there are 120 left-handers,
then how many right-handers are there
6 : 15 :: 120 : x
product of extremes = product of means
a:b = c:d
$\frac{a}{b}$ = $\frac{c}{d}$
ad = bc
a = 6, b = 15, c = 120, d = x
6x = 15 x 120
4x = 1800
x = $\frac{1800}{6}$
x = 300

Question 46.
Mrs. Jackson gave a sum of money to her son and daughter in the ratio 8 : 9. Her daughter received $3,060. How much did Mrs. Jackson give to her two children in all? (Chapter 4)
Answer:
$5,780
Explanation:
Mrs. Jackson gave a sum of money to her son and daughter in the ratio 8 : 9.
Her daughter received $3,060.
Her son received
8 : 9 = 3060 : x
$\frac{8}{9}$ = 3060
9x = 3060 x 8
x = 24480 ÷ 9
x = 2720
Total amount Mrs. Jackson give to her two children in all
= 3060 + 2720
= 5780

Question 47.
The ratio of the number of boys to the number of girls in a school is 7 : 9. If there are 1,248 students in the school, how many girls are there? (Chapter 4)
Answer:
702 girls
The ratio of the number of boys to the number of girls in a school is 7 : 9.
If there are 1,248 students in the school,
Let the number of boys be 7x and girls be 9x
Total number of students = 7x + 9x = 1248
=> 16x = 1248
x = 1248 ÷ 16
x = 78
Number of girls = 9x
= 9 x 78 = 702

Question 48.
A sum of money was shared among Daniel, Elliot, and Frank in the ratio 5 : 7 : 8. If Frank’s share was $2,781 more than Daniel’s share, what was the original sum of money shared among the three men? (Chapter 4)
Answer:
$18540
Explanation:
Let 5x = Daniel’s share
7x = Elliot’s share
8x = Frank’s share
8x = 5x + 2781
3x = 2781
x = 927
Daniel’s share = 5x
= 5 × 927 = $4635
Elliot’s share = 7x
= 7 × 927 = $6489
Frank’s share = 8x
= 8 × 927 = $7416
Amount shared among all = 4635 + 6489 + 7416 = $18540

Question 49.
A tank is filled with water at a rate of 2.4 liters per minute. At this rate, how long will it take to fill the tank with 84 liters of water? (Chapter 5)
Answer:
35 minutes
Explanation:
A tank is filled with water at a rate of 2.4 liters per minute.
At this rate, how long will it take to fill the tank with 84 liters of water
1 min = 2.4 L
84 L = x
x = 84 ÷ 2.4
x = 35min

Question 50.
A farmer uses 920 grams of grains to feed 8 chickens. (Chapter 5)
a) At this rate, how many grams of grains does he use to feed 100 chickens?
Answer:
11500 grams
Explanation:
number of grams used to feed 8 chickens = 920g
number of grams used to feed 1 chicken = 920 ÷ 8 = 115g
number of grams used to feed 100 chickens = 100 × grams used for 1 chicken
= 100 × 115 = 11500g

b) At this rate, how many chickens can he feed using 48.3 kilograms of grains?
Answer:
420 chickens
Explanation:
Grams used = 48.3 × 1000 = 48300g
1kg = 1000g
number of grams used to feed 1 chicken = 115g
number of chickens = grams used ÷ number of grams used to feed 1 chicken
= 48300 ÷ 115
= 420 chickens

Question 51.
The distance between School A and School B is 360 kilometers. (Chapter 5)
a) If a bus leaves School A at 9:30 A.M. and reaches School B at 2:30 P.M., what is its speed in kilometers per hour?
Answer:
A to B = 360Km
Explanation:
start time at A 9:30 AM
reaching time at B 2:30 PM
the difference = 5Hours
Speed = $\frac{Distance}{Time}$
= $\frac{360}{5}$
= 72 kilometers per hour

b) If a car travels at a speed of 80 kilometers per hour, how long will it take to travel from School A to School B?
Answer:
400 kilometer
Explanation:
start time at A 9:30 AM
reaching time at B 2:30 PM
speed of car is 80kilometer per hour
Speed = $\frac{Distance}{Time}$
80 = $\frac{Distance}{5}$
80 × 5 = Distance
Distance travels by a car = 400 kilometers

Question 52.
A truck traveled from Town A to Town B, and then to Town C. The truck took 3 hours to travel from Town A to Town B at an average speed of 42 kilometers per hour. It then traveled from Town B to Town C at an average speed of 68 kilometers per hour. The truck took a total of 5 hours to travel from Town A to Town C. (Chapter 5)
a) What is the distance between Town A and Town B?
Answer:
126km
Explanation:
Town A to Town B
time = 3hours and (speed = 42 kmph)
the distance between Town A and Town B
Distance = Speed x time
= 42 × 3
= 126 kilometers
the distance between Town A and Town B is 126 km

b) What was average speed of the truck for the whole journey?
Answer:
55 kilometers per hour
Explanation:
(42 + 68)/2
= 110/2
= 55 kilometers per hour

Question 53.
Russell bought a CD player that cost $120 before it went on sale for a 15% discount. If he paid 5% sales tax on the sale price, how much did Russell pay for the CD player? (Chapter 6)
$Math in Focus Grade 6 Cumulative Review Chapters 4-7 Answer Key 2$
Answer:
$107.10
Explanation:
Russell bought a CD player that cost $120,
before it went on sale for a 15% discount.
If he paid 5% sales tax on the sale price, how much did Russell pay for the CD player
(120 × 15)/100
= 18
= 120 – 18
= 102
= (102 × 5)/100
= 510/100
= 5.1
Russell pay for the CD player
= $102 + $5.1
= $107.10

Question 54.
Last year, Jane had $2,800 in her bank account. This year, her savings increased by 4.5%. $he plans to increase her savings by 5% next year. How much will Jane have in her account after the two-year period? (Chapter 6)
Answer:
$3,072.30
Explanation:
Jane had $2,800 in her bank account.
(2,800 × 4.5)/100
=12,600/100
=126
2,800 + 126 = 2,926
= (2,926 × 5 )/100
= 14,630/100
= 146.3
2926 + 146.3
= 3,072.3

Question 55.
Two jackets were on sale. The first jacket cost $239 and was marked down 40%. The second jacket cost $159 and was given a 20% discount. Which of the two jackets cost less during the sale? Justify your reasoning. (Chapter 6)
Answer:
Second jacket
Explanation:
The first jacket cost $239 and was marked down 40%.
100 – 40 = 60%
60% of 239
(60 ÷ 100) × 239 = 143.40
The second jacket cost $159 and was given a 20% discount
100 – 20 = 80%
80% of 159
(80 ÷ 100) × 159 = 127.20
By compare the price of both the jackets,
second jacket price is less than the first one.

Question 56.
One year, the price of a motorcycle was $3,000. It increased to $3,550 another year. What is the percent increase in its price? Round your answer to 2 decimal places. (Chapter 6)
Answer:
18.33 or 18%
Explanation:
the price of a motorcycle was $3,000.
It increased to $3,550 another year.
the price in second year increased = 3550 – 3000 = 550
the percent increase in its price
1 – (3550 ÷ 3000)
= 1 – 1.1833
= 1833 ÷ 100 = 18.33

Question 57.
Leonard has 5 times as many stamps as Alison. Melissa has 7 more stamps than Leonard. If Alison has q stamps, how many stamps does Melissa have? (Chapter 7)
Answer:
5q + 7 stamps
Explanation:
A ⇒ q
L ⇒ 5q
M ⇒5q + 7
Melissa have 5q + 7 stamps

Question 58.
Tim is k years old and Jennifer is 4 years younger than Tim. Find their average age in 3k years’ time, in terms of k. (Chapter 7)
Answer:
(4k – 2) years
Explanation:
Tim k years
Jennifer is k – 4
average age in 3k years
= (k + 3k +k – 4 + 3k)/2
= 8k – 4/2
= 2(4k – 2)/2
= 4k – 2

Question 59.
The length of a rectangular garden is 7 meters longer than its width. If its perimeter is (12x + 14) meters, find its length in terms of x. (Chapter 7)
Answer:
(3x + 7)m
Explanation:
Perimeter of rectangle = 2 (length +width)
12x + 14 = 2 (x + 7 + x)
Perimeter = 2 width + 2 length
12x + 14 = 2 length + 2x
12x – 2x + 14 = 2 length
10x + 14 = 2 length
length = 2(5x+ 7)/2
= 5x+7

Question 60.
A cupboard weighs (5y + 6) pounds more than a table. 3 cupboards and 4 tables weigh (29y + 18) pounds in all. (Chapter 7)
a) Find the weight of the table in terms of y.
Answer:
2y lb
Explanation:
29y + 18 = 3 cupboards + 4 tables
29y + 18 = 3[( 5y + 6 ) + table] + 4 tables
29y + 18 =15y + 18 + 3 tables + 4 tables
29y – 15y +18 – 18 = 7 tables
14y = 7 tables
table = 2y

b) If y = 15, find the total weight of 2 cupboards and 3 tables.
Answer:
312 lb
Explanation:
y = 15
2[( 5y + 6 ) + table] + 3 tables
2[( 5y + 6 ) + 2y] + 3 × 2y
for y = 15
10y + 12 + 4y + 6y
20y +12
= 20(15) + 12
= 300 + 12
= 312 lbs

Question 61.
A factory can produce 45 containers of yogurt in t minutes. 950 grams of fruit are used for every 25 containers of yogurt. (Chapters 5, 7)
a) Find, in terms of t, the number of containers of yogurt that the factory can produce in 5 minutes.
Answer:
$\frac{225}{t}$ containers
Explanation:
45 containers in t minutes,
950 grams of fruit are used for every 25 containers of yogurt.
(45 × 5) ÷ t
= $\frac{225}{t}$min

b) Find, in terms of t, the time taken by the factory to produce 100 containers of yogurt.
Answer:
$\frac{20}{9}$min or 2.22min
Explanation:
45 containers in t minutes,
time taken for 100 containers
Time = (100 containers ÷ 45 containers) × t
= $\frac{20}{9}$min or 2.22min

c) If t = 6, find the amount of fruit used in producing containers of yogurt in 8 minutes.
Answer:
2,280 grams
Explanation:
If t = 6min
45 containers in 6min
In 8 min number of containers produced
(45/6min) × 8min = 60 Containers.
the amount of fruit used in producing containers of yogurt in 8 minutes
=(950grams/25cont) × 60 = 2280 Grams

Math in Focus Grade 6 Chapter 7 Lesson 7.4 Answer Key Expanding and Factoring Algebraic Expressions

September 24, 2024September 23, 2024 by Hillary

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Lesson 7.4 Expanding and Factoring Algebraic Expressions to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 7 Lesson 7.4 Answer Key Expanding and Factoring Algebraic Expressions

Math in Focus Grade 6 Chapter 7 Lesson 7.4 Guided Practice Answer Key

Expand each expression.

Question 1.
3(x + 4)
Answer:
3x+12
Explanation:
3(x + 4)
= 3x + 3 x 4
= 3x + 12

Question 2.
6(2x + 3)
Answer:
12x + 18
Explanation:
6(2x + 3)
= 6 X 2x + 6 x 3
= 12x + 18

Question 3.
2(7 + 6x)
Answer: 14+ 12x
Explanation:
2(7 + 6x)
= 2 x 7 + 6x X 2
= 14 + 12x

Question 4.
5(y – 3)
Answer:
5y – 15
Explanation:
5(y – 3)
= 5y-15

Question 5.
4(4y – 1)
Answer:
16y – 4
Explanation:
4(4y – 1)
= 16y – 4

Question 6.
9(5x – 2)
Answer:
45x – 18
Explanation:
9(5x – 2)
= 9 x 5x – 2 x 9
= 45x – 18

State whether each pair of expressions are equivalent.

Question 7.
6(x + 5) and 6x + 30
Answer:
Yes, pair of expressions are equivalent
Explanation:
6(x + 5) and 6x + 30
6(x + 5) = 6x + 30
6(x + 5) and 6x + 30 are equal.

Question 8.
7(x + 3) and 21 + 7x
Answer:
Yes, pair of expressions are equivalent
Explanation:
7(x + 3) and 21 + 7x
7(x + 3) = 7x + 21
7x + 21 and 21 + 7x are equal.

Question 9.
4(y – 4) and 4y – 4
Answer:
NO, pair of expressions are not equivalent
Explanation:
4(y – 4) and 4y – 4
4(y – 4) = 4y – 16
4y – 16 is not equal to 4y – 4

Question 10.
3(y – 6) and 18 – 3y
Answer:
NO, pair of expressions are not equivalent
Explanation:
3(y – 6) and 18 – 3y
3(y – 6) = 3y – 18
3y – 18 is not equal to 18 – 3y

Hands-On Activity

Materials

paper
ruler
scissors

RECOGNIZE THAT EXPANDED EXPRESSIONS ARE EQUIVALENT

STEP 1: Draw a rectangle that is 8 centimeters wide and more than 3 centimeters long on a piece of paper. Then cut out the rectangle.
Answer:
$Math in Focus Grade 6 Chapter 7 Lesson 7.4 Answer Key Expanding and Factoring Algebraic Expressions 1$
STEP 2: Find the area of the rectangle in terms of p.
Answer:
8p + 24 cm
Explanation:
Area of rectangle = Length x Breadth
= (p+3) x 8
= 8p + 24 cm
STEP 3: Then cut the rectangle into two rectangles A and B as shown.
$Math in Focus Grade 6 Chapter 7 Lesson 7.4 Answer Key Expanding and Factoring Algebraic Expressions 2$

STEP 4: Find the areas of rectangle A and rectangle B.
Answer:
24cm
Explanation:
Area of rectangle A = Length x Breadth
= p x 8
= 8p cm
Area of rectangle B = Length x Breadth
= 3 x 8
= 24 cm

STEP 5: Using your answers found in STEP 2 and STEP 4, state how the three areas are related.
Answer:
8p + 24 cm
Explanation:
Area of rectangle = Area of rectangle A + Area of rectangle B
8p + 24 cm = 8p + 24 cm

STEP 6: You may repeat the activity using rectangles of other sizes.
can be done with different size of rectangles

Factor each expression.

Question 11.
3x + 3
Answer:
3,(x + 1)
Explanation:
In the above expression 3 is common factor.
3 and (x + 1) are the factors of 3x + 3

Question 12.
4x + 6
Answer:
2 and (2x + 3)
Explanation:
In the above expression 2 is common factor.
2,(2x + 3) are the factors of 4x + 6

Question 13.
8 + 6y
Answer:
2 and (4 + 3y)
Explanation:
8+6y
In the above expression 2 is common factor.
2 and (4 + 3y) are the factors of 8 + 6y

Question 14.
5y – 10
Answer:
5, (y-2)
Explanation:
In the above expression 5 is common factor.
5y – 10 = 5(y – 2)

Question 15.
4 – 10z
Answer:
2(2 – 5z)
Explanation:
In the above expression 2 is common factor.
4 – 10z = 2(2 – 5z)

Question 16.
12 – 8x
Answer:
4, (3-2x)
Explanation:
In the above expression 4 is common factor.
12 – 8x = 4(3 – 2x)

Question 17.
8f + 6
Answer:
2 ,(4f+3)
Explanation:
In the above expression 2 is common factor.
8f + 6 = 2(4f + 3)

Question 18.
12t – 8
Answer:
4,(3f – 2)
Explanation:
In the above expression 4 is common factor.
12t – 8 = 4(3f – 2)

Question 19.
15 + 5q
Answer:
5, (3+q)
Explanation:
In the above expression 5 is common factor.
15 + 5q = 5(3 + q)

Question 20.
32m – 40
Answer:
8 and (4m-5)
Explanation:
In the above expression 8 is common.
8 and (4m – 5)are the factors of 32m – 40

State whether each pair of expressions are equivalent.

Question 21.
8x + 6 and 2(4x + 3)
Answer:
Yes, pair of expressions are equivalent.
Explanation:
8x + 6 and 2(4x + 3)
8x + 6 = 2(4x + 3)
2(4x + 3) and 2(4x + 3) are equal.

Question 22.
3(y + 6) and 18 + 3y
Answer:
Yes, pair of expressions are equivalent.
Explanation:
3(y + 6) and 18 + 3y
3(y + 6) = 3y + 18
3y + 18 = 18 + 3y are equal.

Question 23.
5x – 10 and 5(x – 5)
Answer:
No, pair of expressions are not equivalent.
Explanation:
5x – 10 and 5(x – 5)
5x – 10 = 5(x – 2)
5(x – 2) and 5(x – 5) are not equal.

Question 24.
4(y – 4) and 16 – 4y
Answer:
No, pair of expressions are not equivalent.
Explanation:
4(y – 4) and 16 – 4y
4(y – 4) = 4y – 16
4y – 16 is not equivalent to 16 – 4y
4(y – 4) and 16 – 4y are not equivalent.

Question 25.
3(x + 5) and 15 + 3x
Answer:
Yes, pair of expressions are not equivalent.
Explanation:
3(x + 5) and 15 + 3x
3(x + 5) = 3x + 15
3x + 15 is equal to 15 + 3x
3(x + 5) and 15 + 3x are equivalent expressions.

Question 26.
12 – 8y and 4(2y – 3)
Answer:
No, pair of expressions are not equivalent.
Explanation:
12 – 8y and 4(2y – 3)
12 – 8y = 4(3 – 2y)
12 – 8y and 4(2y – 3) are not equivalent.

Math in Focus Course 1A Practice 7.4 Answer Key

Expand each expression.

Question 1.
5(x + 2)
Answer:
5x + 10
Explanation:
5(x + 2)
= 5 X x + 5 X 2
= 5x + 10

Question 2.
7(2x – 3)
Answer:
14x – 21
Explanation:
7(2x – 3)
= 7 X 2x – 7 X 3
= 14x – 21

Question 3.
4(y – 3)
Answer:
4y – 12
Explanation:
4(y – 3)
= 4 X y – 4 X 3
= 4y – 12

Question 4.
8(3y – 4)
Answer:
24y – 32
Explanation:
8(3y – 4)
= 8 X 3y – 8 X 4
= 24y – 32

Question 5.
3(x+ 11)
Answer:
3x + 33
Explanation:
3(x+ 11)
= 3 X x + 3 X 11
= 3x + 33

Question 6.
9(4x – 7)
Answer:
36x – 63
Explanation:
9(4x – 7)
= 9 X 4x – 9 X 7
= 36 x – 63

Factor each expression.

Question 7.
6p + 6
Answer:
6 , (p + 1)
Explanation:
6p + 6
Take 6 as common factor
6 (p + 1)
6, (p + 1) are the factors of 6p + 6

Question 8.
3p + 18
Answer:
3, (p + 6)
Explanation:
3p + 18
Take 3 as common factor
3 (p + 6)
3, (p+6) are the factors of 3p + 18

Question 9.
12 + 3q
Answer:
3, (4 + q)
Explanation:
12 + 3q
Take 3 as common factor
3 (4 + q)
3, (4 + q) are the factors of 12 + 3q

Question 10.
4w – 16
Answer:
4, (w – 4)
Explanation:
4w – 16
take 4 as common factor,
4 (w – 4)
4, (w – 4) are the factors of 4w – 16

Question 11.
14r – 8
Answer:
2, (7r – 4)
Explanation:
14r – 8
take 2 as common factor,
2 (7r – 4)
2, (7r – 4) are the factors of 14r – 8

Question 12.
12r – 12
Answer:
12, (r – 1)
Explanation:
12r – 12
take 12 as common factor,
12 (r – 1)
12, (r – 1) are the factors of 12r – 12

State whether each pair of expressions are equivalent.

Question 13.
4x + 12 and 4(x + 3)
Answer:
YES, pair of expressions are equivalent
Explanation:
4x + 12 and 4(x + 3)
4x + 12 and 4x + 12
both are equal

Question 14.
5(x – 1) and 5x – 1
Answer:
NO, pair of expressions are not equivalent
Explanation:
5(x – 1) and 5x – 1
5x – 5 and 5x – 1
both are not equal

Question 15.
7(5 + y) and 7y + 35
Answer:
YES, pair of expressions are equivalent
Explanation:
7(5 + y) and 7y + 35
35 + 7y and 7y + 35
both are equal

Question 16.
9(y – 2) and 18 – 9y
Answer:
NO, pair of expressions are not equivalent
Explanation:
9(y – 2) and 18 – 9y
9y – 18 and 18 – 9y
both are not equal

Expand and simplify each expression.

Question 17.
3(m + 2) + 4(6 + m)
Answer:
7m + 30
Explanation:
3(m + 2) + 4(6 + m)
= 3m + 6 + 24 +4m
= 7m + 30

Question 18.
5(2p + 5) + 4(2p – 3)
Answer:
18p+13
Explanation:
5(2p + 5) + 4(2p – 3)
= 10p + 25 + 8p – 12
= 18p + 13

Question 19.
4(6k + 7)+ 9 – 14k
Answer:
10k + 37
Explanation:
4(6k + 7)+ 9 – 14k
= 24k + 28 + 9 – 14k
= 10k + 37

Simplify each expression. Then factor the expression.

Question 20.
14x + 13 – 8x – 1
Answer:
6, (x+2)
Explanation:
14x + 13 – 8x – 1
= 14x – 8x + 13 – 1
= 6x + 12
= 6(x + 2)
6, (x + 2) are the factors of 14x + 13 – 8x – 1

Question 21.
8(y + 3) + 6 – 3y
Answer:
5, (y+6)
Explanation:
8(y + 3) + 6 – 3y
= 8y + 24 + 6 – 3y
= 8y – 3y + 24 + 6
= 5y + 30
= 5(y + 6)
5, (y + 6) are the factors of the 8(y + 3) + 6 – 3y

Question 22.
4(3z + 7) + 5(8 + 6z)
Answer:
2 , (21z+34)
Explanation:
4(3z + 7) + 5(8 + 6z)
= 12z + 28 + 40 + 30z
= 12z + 30z + 40 + 28
= 42z + 68
= 2 (21z + 34)
2 , (21z + 34) are the factors of 4(3z + 7) + 5(8 + 6z)

Solve.

Question 23.
Expand and simplify the expression 3(x – 2) + 9(x + 1) + 5(1 + 2x) + 2(3x – 4).
Answer:
28x
Explanation:
3(x – 2) + 9(x + 1) + 5(1 + 2x) + 2(3x – 4).
= 3x – 6 + 9x + 9 + 5 + 10x + 6x – 8.
= 3x + 9x + 10x + 6x – 6 +9 +5 – 8
= 28x + 0
= 28x

Question 24.
Are the two expressions equivalent? Justify your reasoning.
15(y + 6) + 10(y – 5) + 20(2y + 3)and 5(20 + 13y)
Answer:
Yes, the two expressions equivalent
Explanation:
15(y + 6) + 10(y – 5) + 20(2y + 3) and 5(20 + 13y)
= 15(y + 6) + 10(y – 5) + 20(2y + 3) and 5(20 + 13y)
= 15y + 90 + 10y – 50 +40y + 60 and 100 + 65y
= 65y + 100 and 100 + 65y
So, both are same.

Question 25.
A yard of lace costs w cents and a yard of fabric costs 40c more than the lace. Kimberly wants to buy one yard of lace and 2 yards of fabric. How much money will she need? Express your answer in terms of w.
Answer:
$80 w cents
Explanation:
cost of one yard of lace = w cents
cost of 2 yards of fabric = 2 × 40 = $80
Therefore, the total money needed is $80 + w cents
= $80 w cents

Question 26.
The average weight of 6 packages ¡s (9m + 8) pounds. 2 more packages, with weights of (12m + 1 2) pounds and (14m + 12) pounds, are added to the original 6 packages. Find the average weight of the 8 packages.
Answer:
10m + 9
Explanation:
9m + 8 is the average weight of the 6 packages = 54m + 48
12m + 12 and 14m + 12 is added
12m+12+14m+12 = 26m + 24
26m + 24 is added to the 54m + 48
= 54m + 26m + 48 + 24
= 80m + 72
the average weight of the 8 packages is = (80m + 72)/8 = 10m + 9

Question 27.
The figure shows two rectangles joined to form rectangle ABCD.
$Math in Focus Grade 6 Chapter 7 Lesson 7.4 Answer Key Expanding and Factoring Algebraic Expressions 3$
a) Write the length of $\overline{B C}$ in terms of x. Then write an expression for the area of the rectangle ABCD in terms of x.
Answer:
Area =3x + 6 cm
Explanation:
the length of $\overline{B C}$ in terms of x = x + 2
an expression for the area of the rectangle ABCD in terms of x
= x + 2 X 3
= (x + 2)3
= 3x + 6cm

b) Write an expression for the area of each of the two smaller rectangles.
Answer:
6 cm
Explanation:
the area of each of the two smaller rectangles
= 2 x 3 = 6cm

c) Math Journal Explain how you can use your answers in a) and b) to show that the following expressions are equivalent. 3x + 6 and 3(x + 2)
Answer:
Yes, both are equivalent
Explanation:
3x + 6 and 3(x + 2)
3(x + 2) can be written as 3x + 6
So, both are equal.

Math in Focus Grade 6 Chapter 7 Lesson 7.2 Answer Key Evaluating Algebraic Expressions

September 24, 2024September 23, 2024 by Hillary

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Lesson 7.2 Evaluating Algebraic Expressions to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 7 Lesson 7.2 Answer Key Evaluating Algebraic Expressions

Math in Focus Grade 6 Chapter 7 Lesson 7.2 Guided Practice Answer Key

Evaluate each algebraic expression for the given value of x.

Question 1.
$Math in Focus Grade 6 Chapter 7 Lesson 7.2 Answer Key Evaluating Algebraic Expressions 1$
Answer:

Explanation:
An expression is a term in that describes a group of variables, numbers and operators.
Operators include division, multiplication, addition and subtraction.
Variables in expression are usually denoted as x and y, but it can be and other symbol.
The expressions can be written as verbal phrase or algebraic expression.

Math in Focus Course 1A Practice 7.2 Answer Key

Evaluate each expression for the given value of the x.

Question 1.
x + x + 5 when x = 7
Answer:
19
Explanation:
x = 7
by substituting x value as 7
x + x + 5 = 7 + 7 + 5 = 19

Question 2.
3x + 5 when x = 5
Answer:
20
Explanation:
3x + 5, where as
x = 5
by substituting x value =5
3 x 5 + 5 = 15 + 5 = 20

Question 3.
5y – 8 when y = 3
Answer:
7
Explanation:
5 x y – 8
y = 3
by substituting y value = 3
5 x 3 – 8
15 – 8 = 7

Question 4.
40 – 9y when y = 2
Answer:
22
Explanation:
40 – 9y
y = 2
by substituting y value = 2
40 – 9 x 2 = 40 – 18 = 22

Question 5.
33 – 7w + 6 when w = 4
Answer:
19
Explanation:
33 – 7w + 6
w = 4
by substituting w value = 4
33 – 7 x 4 = 33 – 14 = 19

Question 6.
$\frac{7w}{2}$ when w = 18
Answer:
63
Explanation:
= $\frac{7w}{2}$
w = 18
by substituting w value = 18
= $\frac{7 x 18}{2}$
= $\frac{126}{2}$ = 63

Question 7.
4 + $\frac{5z}{6}$ when z = 12
Answer:
14
Explanation:
4 + $\frac{5z}{6}$
z = 12
by substituting z value = 12
= 4 + $\frac{5×12}{6}$
= 4 + $\frac{60}{6}$
= 4+10 = 14

Question 8.
$\frac{4+5z}{2}$ when z = 12
Answer:
32
Explanation:
$\frac{4+5z}{2}$
z = 12
by substituting z value =12
= $\frac{4+5 x 12}{2}$
= $\frac{4+60}{2}$
= $\frac{64}{2}$ = 32

Question 9.
20 – $\frac{4r}{5}$ when r = 10
Answer:
16
Explanation:
20 – $\frac{4r}{5}$
r = 10
by substituting r value =10
= 20 – $\frac{4x 10}{5}$
= 20 – $\frac{40}{5}$
= 20 – 8 = 16

Question 10.
$\frac{8r}{9}$ – 15 when r = 27
Answer:
9
Explanation:
$\frac{8r}{9}$ – 15
r = 27
by substituting r value =27
= $\frac{8 x 27}{9}$ – 15
= $\frac{216}{9}$ – 15
24 – 15 = 9

Question 11.
16 – $\frac{2 z-4}{3}$ when z = 18
Answer:
$\frac{16}{3}$
Explanation:
16 – $\frac{2 z-4}{3}$ when z = 18
by substituting z value = 18
16 – $\frac{2 z-4}{3}$
=16 – $\frac{2 x 18 – 4}{3}$
=16 – $\frac{36-4}{3}$
=16 – $\frac{32}{3}$
=$\frac{48-32}{3}$
$\frac{16}{3}$

Question 12.
16 – $\frac{2 z}{3}$ – 4 when z = 18
Answer:
0
Explanation:
16 – $\frac{2 z}{3}$ – 4 when z = 18
by substituting z value = 18
16 – $\frac{2 x 18}{3}$ – 4
= 16 – $\frac{36}{3}$ – 4
=16 – 12 – 4
=0

Evaluate each expression when x = 3.

Question 13.
$\frac{x+1}{2}$ + $\frac{5 x-3}{10}$
Answer:
$\frac{16}{5}$
Explanation:
by substituting x value = 3 in the given algebraic equation
$\frac{x+1}{2}$ + $\frac{5 x-3}{10}$
= $\frac{3+1}{2}$ + $\frac{5 x 3 – 3}{10}$
= $\frac{4}{2}$ + $\frac{12}{10}$
= 2 + $\frac{6}{5}$
= $\frac{10 + 6}{5}$
= $\frac{16}{5}$

Question 14.
$\frac{11+x}{2}$ – $\frac{9 x-3}{4}$
Answer:
1
Explanation:
by substituting x value = 3 in the given algebraic equation
$\frac{11+x}{2}$ – $\frac{9 x-3}{4}$
= $\frac{11+3}{2}$ – $\frac{9 x 3-3}{4}$
= $\frac{14}{2}$ – $\frac{27-3}{4}$
= $\frac{7}{1}$ – $\frac{24}{4}$
7 – 6 = 1

Question 15.
$\frac{7 x-6}{3}$ + 4(8 + 2x)
Answer:
61
Explanation:
by substituting x value = 3 in the given algebraic equation
$\frac{7 x-6}{3}$ + 4(8 + 2x)
= $\frac{7 x 3 -6}{3}$ + 4(8 + 2 x 3)
= $\frac{21- 6}{3}$ + 4(8 + 6)
= $\frac{15}{3}$ + 56
= 5 + 56
= 61

Question 16.
13(11 – 3x) – $\frac{5(16-4 x)}{2}$
Answer:
16
Explanation:
by substituting x value = 3 in the given algebraic equation
13(11 – 3x) – $\frac{5(16-4 x)}{2}$
13(11 – 3 x 3) – $\frac{5(16-4 x 3)}{2}$
13(11 – 9) – $\frac{5(16 – 12)}{2}$
13(2) – $\frac{5(4)}{2}$
26 – $\frac{20}{2}$
= 26 – $\frac{20}{2}$
= 26 – 10
= 16

Question 17.
5(x + 2) + 2(6 – x) + $\frac{2 x+3}{3}$
Answer:
34
Explanation:
by substituting x value = 3 in the given algebraic equation
5(x + 2) + 2(6 – x) + $\frac{2 x+3}{3}$
5(3 + 2) + 2(6 – 3) + $\frac{2 x 3+3}{3}$
5(5) + 2(3) + $\frac{6+3}{3}$
25 + 6 + 3 = 34

Question 18.
$\frac{5 x-3}{4}$ + $\frac{5(x+5)}{8}$ + 3(13 – 2x)
Answer:
29
Explanation:
by substituting x value = 3 in the given algebraic equation
$\frac{5 x-3}{4}$ + $\frac{5(x+5)}{8}$ + 3(13 – 2x)
= $\frac{5 x 3 – 3}{4}$ + $\frac{5(3+5)}{8}$ + 3(13 – 2 x 3)
= $\frac{15-3}{4}$ + $\frac{5(8)}{8}$ + 3(13 – 6)
= $\frac{12}{4}$ + $\frac{40}{8}$ + 3(7)
= 3 + 5 + 21
= 29

Question 19.
$\frac{2 x+4}{5}$ – $\frac{x+1}{4}$ + $\frac{x}{6}$
Answer:
$\frac{3}{2}$
Explanation:
by substituting x value = 3 in the given algebraic equation
$\frac{2 x+4}{5}$ – $\frac{x+1}{4}$ + $\frac{x}{6}$
= $\frac{2 x 3+4}{5}$ – $\frac{3+1}{4}$ + $\frac{3}{6}$
= $\frac{10}{5}$ – $\frac{4}{4}$ + $\frac{1}{2}$
= 2-1+$\frac{1}{2}$
=1+$\frac{1}{2}$
= $\frac{3}{2}$

Question 20.
7x – $\frac{x}{5}$ + $\frac{7-x}{9}$
Answer:
21 – $\frac{3}{5}$ + $\frac{4}{9}$
Explanation:
by substituting x value = 3 in the given algebraic equation
7x – $\frac{x}{5}$ + $\frac{7-x}{9}$
= 7 x 3 – $\frac{3}{5}$ + $\frac{7-3}{9}$
= 21 – $\frac{3}{5}$ + $\frac{4}{9}$
= 21 – $\frac{3}{5}$ + $\frac{4}{9}$

Evaluate each of the following when y = 7.

Question 21.
(5y + 2) minus (2y + 5).
Answer:
18
Explanation:
by substituting y value = 7 in the given algebraic equation
(5y + 2) minus (2y + 5)
= (5 x 7 + 2) – (2 x 7 + 5).
= (35 + 2) – (14 + 5).
= 37 – 19
= 18

Question 22.
The sum of $\frac{y}{3}$ and $\frac{4y}{9}$
Answer:
$\frac{49}{9}$
Explanation:
by substituting y value = 7 in the given algebraic equation
$\frac{y}{3}$ + $\frac{4y}{9}$
= $\frac{7}{3}$ + $\frac{4 x 7}{9}$
= $\frac{7}{3}$ + $\frac{28}{9}$
= $\frac{21+28}{9}$
= $\frac{49}{9}$

Question 23.
The product of (y + 1)and(y – 1)
Answer:
$\frac{4}{3}$
Explanation:
by substituting y value = 7 in the given algebraic equation
(y + 1)and(y – 1)
= (7 + 1)and(7 – 1)
= (8)and(6)
= $\frac{8}{6}$
= $\frac{4}{3}$

Question 24.
8(2y – 1) minus $\frac{14 y+37}{5}$
Answer:
8(2y – 1) minus $\frac{14 y+37}{5}$
Explanation:
by substituting y value = 7 in the given algebraic equation
8(2y – 1) minus $\frac{14 y+37}{5}$
= 8(2 X 7 – 1) minus $\frac{14 X 7 + 37}{5}$
= 8(2y – 1) minus $\frac{14 y+37}{5}$

Question 25.
The quotient of 9(7y – 15) and $\frac{110-6 y}{4}$
Answer:
18
Explanation:
by substituting y value = 7 in the given algebraic equation
9(7y – 15) and $\frac{110-6 y}{4}$
= 9(7 x 7 – 15) and $\frac{110 – 6 x 7}{4}$
= 9(49 – 15) and $\frac{110-42}{4}$
= 9(34) and $\frac{68}{4}$
= 306/17 = 18

Question 26.
The sum of $\frac{5 y}{6}$ and 4($\frac{3 y}{7}$ + 2y)
Answer:
$\frac{443}{6}$
Explanation:
by substituting y value = 7 in the given algebraic equation
$\frac{5 y}{6}$ and 4($\frac{3 y}{7}$ + 2y)
= $\frac{5 x 7}{6}$ and 4($\frac{3 x 7}{7}$ + 2 x 7)
= $\frac{35}{6}$ and 4($\frac{21}{7}$ + 14)
= $\frac{35}{6}$ and 4(3 + 14)
= $\frac{35}{6}$ +68
= $\frac{35 + 408 }{6}$
= $\frac{443}{6}$

Question 27.
The quotient of ($\frac{y}{2}+\frac{2 y}{3}$) and ($\frac{5 y}{6}-\frac{y}{3}$)
Answer:
$\frac{7}{3}$
Explanation:
by substituting y value = 7 in the given algebraic equation
($\frac{y}{2}+\frac{2 y}{3}$) and ($\frac{5 y}{6}-\frac{y}{3}$)
= ($\frac{7}{2}+\frac{2 x 7}{3}$) and ($\frac{5 x 7}{6}-\frac{7}{3}$)
= ($\frac{7}{2}+\frac{14}{3}$) and ($\frac{35}{6}-\frac{7}{3}$)
= ($\frac{21 + 28}{6}$) and ($\frac{35 – 14}{6}$)
= ($\frac{49}{6}$) and ($\frac{21}{6}$)
= ($\frac{49}{6}$) X ($\frac{6}{21}$)
= $\frac{49}{21}$
= $\frac{7}{3}$

Math in Focus Grade 6 Chapter 6 Review Test Answer Key

September 24, 2024September 23, 2024 by Hillary

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 6 Review Test to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 6 Review Test Answer Key

Concepts and Skills

Express each percent as a fraction In simplest form.

Question 1.
46%
Answer:
$\frac{23}{50}$
Explanation:
Divide the given percent by 100 to get the decimal number $\frac{p e r c e n t}{100}$ .
$\frac{46}{100}$
simplify the fraction with the greatest common factor on both sides.
So, 2 is the greatest common factor.
$\frac{23}{50}$

Question 2.
16%
Answer:
$\frac{1}{5}$
Explanation:
Divide the given percent by 100 to get the decimal number $\frac{p e r c e n t}{100}$ .
$\frac{16}{100}$
Simplify the fraction with the greatest common factor on both sides.
So, 4 is the greatest common factor.
$\frac{1}{5}$

Question 3.
88%
Answer:
$\frac{22}{25}$
Explanation:
Divide the given percent by 100 to get the decimal number $\frac{p e r c e n t}{100}$ .
$\frac{88}{100}$
Simplify the fraction with the greatest common factor on both sides.
So, 4 is the greatest common factor.
$\frac{22}{25}$

Express each percent as a decimal.

Question 4.
34%
Answer:
0.34
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
$\frac{34}{100}$ = 0.34

Question 5.
60%
Answer:
0.60
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
$\frac{60}{100}$ = 0.60

Question 6.
9%
Answer:
0.09
Explanation:
In order to convert percent to decimal number,
percentage should be divided by 100.
$\frac{9}{100}$ = 0.09

Express each fraction as a percent.

Question 7.
$\frac{17}{20}$
Answer:
85%
Explanation:
Divide the numerator by the denominator
Multiply the resulting decimal of the above division by 100
Express the value using the symbol “%”
$\frac{17}{20}$ = 0.85
= 0.85 x 100 = 85%

Question 8.
$\frac{21}{25}$
Answer:
48%
Explanation:
Divide the numerator by the denominator
Multiply the resulting decimal of the above division by 100
Express the value using the symbol “%”
$\frac{21}{25}$ = 0.48
= 0.48 x 100 = 48%

Question 9.
$\frac{270}{300}$
Answer:
90%
Explanation:
Divide the numerator by the denominator
Multiply the resulting decimal of the above division by 100
Express the value using the symbol “%”
$\frac{270}{300}$ = 0.9
= 0.9 x 100 = 90%

Express each decimal as a percent.

Question 10.
0.02
Answer:
2%
Explanation:
Convert a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.02 x 100 = 2

Question 11.
0.63
Answer:
63%
Explanation:
Convert a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.63 x 100 = 63

Question 12.
0.9
Answer:
90%
Explanation:
Convert a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.9 x 100 = 90

Find the quantity represented by each percent.

Question 13.
35% of 500 kilograms
Answer:
175 kg
Explanation:
finding the fraction of a number is same as multiplying the fraction with the number, we have.
$\frac{35}{100}$ x 500
= 35 x 5 = 175

Question 14.
68% of $2,800
Answer:
$1,904
Explanation:
finding the fraction of a number is same as multiplying the fraction with the number, we have.
$\frac{68}{100}$ x 2,800
=68 x 28
= 1,904

Solve. Show your work.

Question 15.
There were 45 adults on a bus. 60% of them were women. How many women were on the bus?
Answer:
27 women
Explanation:
Number of adults in bus = 40
60% of them were women.
Total women in bus,
$\frac{60}{100}$ x 45
= $\frac{6}{10}$ x 45
= $\frac{270}{10}$ = 27

Question 16.
Iris had $900. She spent 22% of this amount on a mobile phone. How much did she pay for the mobile phone?
Answer:
$198
Explanation:
Iris had $900.
She spent 22% of this amount on a mobile phone.
Amount she paid for the mobile phone,
$\frac{22}{100}$ x 900
=22 x 9 = 198

Question 17.
22% of a number is 44. Find the number.
Answer:
200 is the number
Explanation:
Let the number be x
44 = x x $\frac{22}{100}$
44 = $\frac{22x}{100}$
22x = 44 x 100
x = $\frac{4400}{22}$
x = 200

Question 18.
125% of a number is 65. Find the number.
Answer:
52 is the number
Explanation:
Let the number be x
65 = x x $\frac{125}{100}$
65 = $\frac{125x}{100}$
125x = 65 x 100
x = $\frac{6500}{125}$
x = 52

Problem Solving

Solve. Show your work.

Question 19.
Harold had 1,400 stamps. He gave 350 of them to his brother and the rest to his sister.
a) What percent of the stamps did he give to his brother?
Answer:
25%
Explanation:
Harold had 1,400 stamps.
He gave 350 of them to his brother
$\frac{350}{1,400}$ x 100
= $\frac{350}{14}$
= 25

b) What percent of the stamps did he give to his sister?
Answer:
75%
Explanation:
Harold had 1,400 stamps.
He gave 350 of them to his brother and rest to his sister
1,400 – 350 = 1,050
$\frac{1,050}{1,400}$ x 100
= $\frac{1,050}{14}$
= 75

Question 20.
There were 15 girls and 25 boys in the Science club. What percent of the members were girls?
Answer:
37.5%
Explanation:
Total students in science club 15 + 25 = 40
Percent of the girls = $\frac{15}{40}$ x 100
= $\frac{1,500}{40}$
= 37.5

Question 21.
Tyrone paid $2,800 plus 7% sales tax on mountain bikes for a bike club. How much did Tyrone pay in total for the mountain bikes?
Answer:
$2996
Explanation:
Tyrone paid $2,800 plus 7% sales tax on mountain bikes for a bike club.
Amount paid by Tyrone for the mountain bikes
2,800 x $\frac{7}{100}$ = 196
= 2800 + 196
= 2996

Question 22.
Howard opens a savings account with a deposit of $800. The bank will pay him 3% interest per year.
a) How much interest will Howard receive at the end of $\frac{1}{2}$ year?
Answer:
$120
savings account with a deposit of $800
3% interest per year
SI = $\frac{P R T}{100}$
= $\frac{800 x 3 x 0.5}{100}$ = 120
for 6 months $120

b) How much interest will he receive at the end of 1 year?
Answer:
$240
Explanation:
SI (simple intrest)= $\frac{P R T}{100}$
= $\frac{800 x 3 x 1}{100}$ = 240
for 1 year $240

Question 23.
A grocery shop sells walnuts at a 40% markup. The shop pays $4.50 per pound for the walnuts. At what price per pound will the shop sell the walnuts?
Answer:
$6.30
Explanation:
The shop pays $4.50 per pound for the walnuts.
A grocery shop sells walnuts at a 40% markup.
profit = 4.50 x $\frac{40}{100}$
p = $\frac{180}{100}$ = 1.8
selling price = 4.50 + 1.80 = 6.30

Question 24.
Inez earns $160 per month by babysitting. She saves 25% of her monthly salary. If her salary increases by 10%, how much will she now save each month?
Answer:
$44
Explanation:
Initial salary = $160
she gives = $\frac{25}{100}$ x 160 = 40
New monthly salary = 160 + $\frac{10}{100}$ x 160 = 176
she saves = $\frac{25}{100}$ x 176 = 44

Question 25.
Last year, Manuel saved $50 per month. This year, he increases his monthly savings by 25%. He plans to buy a smart phone for $375. At this rate, how long will it take him to save enough money to buy the smart phone if he starts saving for it this year?
Answer:
6 months
Explanation:
interest is increased by 25% or $\frac{25}{100}$
= $\frac{1}{4}$
50 time of $\frac{1}{4}$ = $\frac{50}{4}$ = 12.5
So, $\frac{50}{12.5}$ = 62.5 per month
$\frac{375}{62.5}$ = 6 months

Question 26.
The original price of a watch was $550. During a mid-year sale, the selling price of the watch was $440. Find the percent discount.
Answer:
20%
Explanation:
The discount amount is $550 – $440 = $110
Let x represent the unknown percent discount.
550x = 11,000
x = $\frac{11,000}{550}$
x = 20%

Question 27.
In January, the price of a kilogram of Brand X rice was $7.60. In May, the price of a kilogram of Brand X rice became $8.80. Find the percent increase in price. Round your answer to 2 decimal places.
Answer:
$15.79
Explanation:
In January, the price of rice was $7.60.
In May, the price of rice became $8.80.
The price increased to $1.80
The percent increase in price = 120%
Original price = $\frac{120}{7.60}$ = 15.789
Round your answer to 2 decimal places = 15.79

Question 28.
A tank contained 35 gallons of water at first. Due to a leak at the bottom of the tank, the amount of water in the tank decreased to 32 gallons after 1 hour. After another hour, the amount of water in the tank was 26 gallons.
a) Find the percent decrease in the amount of water from 35 gallons to 32 gallons. Round your answer to 1 decimal place.
Answer:
1%
Explanation:
A tank contained 35 gallons of water at first.
Due to a leak at the bottom of the tank, the amount of water in the tank decreased to 32 gallons after 1 hour, 35 – 32 = 3 gallons
$\frac{3}{35}$x100 = 1.05% = 1%

b) Find the percent decrease in the amount of water from 32 gallons to 26 gallons. Round your answer to 1 decimal place.
Answer:
19%
Explanation:
At first the water in tank is 32 gallons.
After another hour, the amount of water in the tank was 26 gallons
32 – 26 = 6 gallons
$\frac{6}{32}$x100 = 18.75% = 19%

Math in Focus Grade 6 Chapter 6 Lesson 6.4 Answer Key Real-World Problems: Percent

September 24, 2024September 23, 2024 by Hillary

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 6 Lesson 6.4 Real-World Problems: Percent to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 6 Lesson 6.4 Answer Key Real-World Problems: Percent

Math in Focus Grade 6 Chapter 6 Lesson 6.4 Guided Practice Answer Key

Solve.

Question 1.
Mr. Jefferson is making 80 cups of fruit punch for the grand opening of his bakery. He uses 52 cups of fruit juice and the rest is sparkling water.
a) What percent of the punch is fruit juice?
Method 1
Fraction of fruit juice in punch = $\frac{?}{?}$
Percent of fruit juice in punch = $\frac{?}{?}$ × $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %
= $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %
= $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ % of the punch is fruit juice.

Method 2
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ cups → 100%
1 cup → $\frac{100}{?}$%
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ cups → ? × $\frac{100}{?}$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ % of the punch is fruit juice.
Answer:
65%
Explanation:
Method 1
Fraction of fruit juice in punch = $\frac{52}{80}$
Percent of fruit juice in punch = $\frac{52}{80}$ × 100%
= 65%
= 65% of the punch is fruit juice.

b) What percent of the punch is sparkling water?
100% – $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ % = $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ % of the punch is sparkling water.
Answer:
35%
Explanation:
100% – 65% = 35%
35% of the punch is sparkling water.

Solve. Check for reasonableness.

Question 2.
A laptop computer displayed at a shop costs $720. A sales tax of 7% will be added to the price. What is the total cost of the laptop computer?
Method 1
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 2$
The total cost of the laptop computer is $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ .

Method 2
Sales tax:
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 3$
The total cost of the laptop computer is $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ .
Answer:
$770.40
Explanation:

Question 3.
Dave went to lunch with his friends. The food cost $78.50, and a sales tax of $4.71 was added to the cost of the meal. What was the sales tax rate?
The cost of the food is $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %.
$ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ → $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %
$1 → $\frac{?}{?}$ %
$ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ → $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ × $\frac{?}{?}$ % = $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %
The sales tax rate was $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %.
Answer:
6%
Explanation:
The cost of the food is $78.50 %.
$4.71 → 1%
$1 → $\frac{4.71}{78.50}$ %
$100 → 100× $\frac{471}{7850}$ % = 0.06%
The sales tax rate was 6%.

Question 4.
Mr. Diaz earns a 3% commission on all the furniture he sells. If he receives $2,880 in commission, what is the dollar amount of his sales?
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 4$
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ % → $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$
1% → $$\frac{?}{?}$ % = $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ %
100% → 100 × $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ = $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$
The dollar amount of his sales is $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ .
Answer:
$96,000
Explanation:
3% → $2,880
1% → $$\frac{2880}{3}$ % = $960 %
100% → 100 × $ 960= $96,000
The dollar amount of his sales is $96,000.

Solve.

Question 5.
A firm has $30,000 in a bank account at the beginning of the year. Interest will be paid at a rate of 2% at the end of the year. How much interest will the firm receive for the year?
Interest = imgg 1 % of $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ for 1 year
= $\frac{?}{?}$ × $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ × 1
= $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$
The firm will receive $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ in interest for the year.
Answer:
$600
Explanation:
Interest = imgg 1 % of $30,000 for 1 year
= $\frac{2}{100}$ × $30,000 × 1
= 2 X 300
= $600

Question 6.
A company has $500,000 in a savings account. The interest is 4% per year. How much interest will it earn at the end of $\frac{1}{2}$ year?
Interest = $\frac{?}{100}$ × $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ × $\frac{?}{?}$
= $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$
The company will earn $ $Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 1$ in interest at the end of $\frac{1}{2}$ year.
Answer:
$10,000
Explanation:
Interest = $\frac{4}{100}$ × $500,000 × $\frac{1}{2}$
= 20,000 X $\frac{1}{2}$
= $10,000
The company will earn $10,000 in interest at the end of $\frac{1}{2}$ year.

Math in Focus Course 1A Practice 6.4 Answer Key

Solve. Show your work. Check that your answers are reasonable.

Question 1.
Ellen had 25 hair clips. 7 of them were blue and the rest were purple.
a) What percent of the hair clips were blue?
Answer:
28%
b) What percent of the hair clips were purple?
Answer:
72%
Explanation:
Ellen had 25 hair clips,
7 of them were blue and the rest were purple.
Number of blue clips = 7
Number of purple clips = 125 – 7 = 18
percentage of blue clips = $\frac{7}{25}$ × 100 = 28%
percentage of purple clips = $\frac{18}{25}$ × 100 = 72%

Question 2.
Gabriel had $60. He spent $36 on a pair of shoes and the rest on a shirt.
$Math in Focus Grade 6 Chapters 6 Lesson 6.4 Answer Key Real-World Problems Percent 5$
a) What percent of the money did he spend on the pair of shoes?
Answer:
60%
b) What percent of the money did he spend on the shirt?
Answer:
40%
Explanation:
Gabriel had $60.
He spent $36 on a pair of shoes and the rest on a shirt.
percent of the money did he spend on the pair of shoes
= $\frac{36}{60}$ × 100
= 60%
Total cost spent on shirt = 60 – 36 = $24
percent of the money did he spend on the shirt
= $\frac{24}{60}$ × 100
= 40%

Question 3.
Ms. Pierce bought a camera that cost $450. In addition, she had to pay 4% u sales tax. How much did Ms. Pierce pay for the camera?
Answer:
$468
Explanation:
Ms. Pierce bought a camera that cost $450.
In addition, she had to pay 4% u sales tax.
Total price of the camera = $\frac{4}{100}$ × 450 = $18
Total amount he paid = camera cost + tax
= $450 + $18 = $468

Question 4.
Mr. Osmond bought a computer that cost $2,500. How much did he pay for the computer if the sales tax rate was 7%?
Answer:
$2,675
Explanation:
Mr. Osmond bought a computer that cost $2,500.
Tax paid for the computer was 7%.
Total amount he paid = $\frac{7}{100}$ × 2,500 = $175
Total amount he paid including tax = cost of computer + tax
= $3,500 + $175 = $2,675

Question 5.
There were 320 girls and 180 boys at a playground. What percent of children were girls?
Answer:
64%
Explanation:
There were 320 girls and 180 boys at a playground.
Total boys and girls = 320 + 180 = 500
percent of children were girls
= $\frac{320}{500}$ × 100 = 64%

Question 6.
Sally spent $36 and had $12 left. What percent of her money did she spend?
Answer:
75%
Explanation:
Sally spent $36 and had $12 left.
Total amount = spent + left
= $36 + $12 = $48
percent of her money did she spend
= $\frac{36}{48}$ × 100 = 75%

Question 7.
An artist receives 20% royalty on the retail price of his recordings. If he receives $36,000 in royalties, what is the dollar amount of the retail price of his recordings?
Answer:
$18,000,000
Explanation:
An artist receives 20% royalty on the retail price of his recordings.
If he receives $36,000 in royalties,
Total dollar amount of the retail price of his recordings
$\frac{20}{100}$ of X = 36,000
100% of X = ?
X = 36000 x $\frac{100}{20}$ x 100
X = 36,000 x 5 x 100
X = 18,000,000

Question 8.
A club deposited $50,000 in a savings account at the beginning of the year. Interest will be paid at a rate of 3% at the end of the year. How much interest will the club receive for the year?
Answer:
$1,500
Explanation:
A club deposited $50,000 in a savings account at the beginning of the year.
Interest will be paid at a rate of 3% at the end of the year.
Total interest will the club receive for the year
= $\frac{3}{100}$ × 50,000 = 1,500

Question 9.
Company X has $128,000 in a savings account that pays 6% interest per year. How much interest will it earn at the end of $\frac{1}{2}$ year?
Answer:
$3,840
Explanation:
Company X has $128,000 in a savings account that pays 6% interest per year.
= $\frac{6}{100}$ × 128,000 = 7,680
Total interest will it earn at the end of $\frac{1}{2}$ year
= $\frac{1}{2}$ × 7,680 = 3,840

Math in Focus Grade 6 Chapter 6 Lesson 6.3 Answer Key Percent of a Quantity

September 24, 2024September 23, 2024 by Hillary

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 6 Lesson 6.3 Percent of a Quantity to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 6 Lesson 6.3 Answer Key Percent of a Quantity

Math in Focus Grade 6 Chapter 6 Lesson 6.3 Guided Practice Answer Key

Complete. Use the models to help you.

Question 1.
What is 40% of 720 centimeters?
Method 1
$Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 1$
The model shows that:
100% → $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ cm
1% → $\frac{?}{?}$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ cm
40% → $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ × $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ cm
40% of 720 centimeters is $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ centimeters.

Method 2
40% of 720 cm = $\frac{?}{100}$ × 720
= $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ cm
40% of 720 centimeters is $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ centimeters.
Answer:
288centimeters
Explanation:
Method 1
The model shows that:
100% → 720cm
1% → $\frac{720}{100}$ = 7.2cm
40% → 7.2 × 40 = 288cm
40% of 720 centimeters is 288 centimeters.

Method 2
40% of 720 cm = $\frac{40}{100}$ × 720
= 288 cm
40% of 720 centimeters is 288centimeters.

Question 2.
What is 75% of 800 kilograms?
Method 1
$Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 3$
The model shows that:
100% → $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ kg
1% → $\frac{?}{?}$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ kg
75% → $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ × $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ kg
75% of 800 kg is $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ kg.

Method 2
75% of 800 kg = $\frac{?}{?}$ × 800
= $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ kg
75% of 800 kg is $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ kg.
Answer:
600kg
Explanation:
The model shows that:
100% → 800kg
1% → $\frac{800}{100}$ = 8kg
75% → 75 × 8 = 600kg
75% of 800 kg is 600kg.

Method 2
75% of 800 kg = $\frac{75}{100}$ × 800
= 600kg
75% of 800 kg is 600kg.

Find the percent of each whole.

Question 3.
30% of 450
Answer: 135
Explanation:
30% of 450
= $\frac{30}{100}$ × 450
= 135
30% of 450 is 135.

Question 4.
225% of $60
Answer: 135
Explanation:
225% of $60
= $\frac{225}{100}$ × 60
= 135
225% of 60 is 135.

Question 5.
55% of 320
Answer: 176
Explanation:
55% of 320
= $\frac{55}{100}$ × 320
= 176
55% of 320 is 176.

Question 6.
110% of $550
Answer: 605
Explanation:
110% of $550
= $\frac{110}{100}$ × 550
= 605
110% of 550 is 605.

Solve. Use the model to help you.

Question 7.
27% of the students in a school are in grade 6. This is 540 students. How many students are there in the school?
$Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 4$
The model shows that:
$Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ % → $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ students
1% → $\frac{?}{?}$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ students
100% → 100 × $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ students
There are $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ students in the school.
Answer:
2000 students.
Explanation:
The model shows that:
27% → 540 students
1% → $\frac{540}{27}$ = 20 students
100% → 100 × 20 = 2000 students
There are 2000 students in the school.

Solve. You may draw a model to help you.

Question 8.
At an amusement park, 60% of the people were adults, and the rest were children. There were 720 adults. How many people were at the amusement park in all?
$Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ % → $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ people
1% → $\frac{?}{?}$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ people
100% → $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ × $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ = $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ people
There were $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ people at the amusement park in all.
Answer:
1200 people
Explanation:
60% → 720people
1% → $\frac{720}{60}$ = 12 people
100% → 100× 12 = 1200 people
There were 1200 people at the amusement park in all.

Find the missing value.

Question 9.
20% of $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ is 163.
Answer: 185
Explanation:
20% of $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ is 163.
$\frac{20}{100}$ x = 163
x = (163 x 100) ÷ 20
= 16300 ÷ 20
= 815

Question 10.
45% of $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ is 150.
Answer: 333
Explanation:
45% of $Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 2$ is 150.
$\frac{45}{100}$ x = 150
x = (150 x 100) ÷ 45
= 15000 ÷ 45
= 333

Math in Focus Course 1A Practice 6.3 Answer Key

Solve. Use the models to help you.

Question 1.
What is 15% of 12 meters?
$Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 5$
Answer: 1.8 m
Explanation:

Question 2.
A park ranger finds that 35% of the park’s visitors stay at the campground. If 105 visitors stayed at the campground one day, how many visitors did the park have that day?
$Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 6$
Answer: 36.75
Explanation:
A park ranger finds that 35% of the park’s visitors stay at the campground.
105 visitors stayed at the campground one day.
number of visitors did the park have that day

Find the quantity represented by each percent.

Question 3.
45% of $360
Answer:
$162
Explanation:
45% of $360
= $\frac{45}{100}$ × 360
= 162
45% of 360 is 162.

Question 4.
66% of 740 kilometers
Answer:
488.4kg
Explanation:
66% of $740
= $\frac{66}{100}$ × 740
= 488.4
66% of 740 is 488.4.

Solve. Show your work.

Question 5.
There are 1,500 students in a school. 65% of them are girls. How many girls are there in the school?
Answer:
975 girls.
Explanation:
There are 1,500 students in a school.
65% of them are girls.
Total girls in the school 65% of 1500
= $\frac{65}{100}$ × 1500
= 975

Question 6.
A school raises $4,000 for its new library. 36% of the money is used to buy reference books. How much money is used to buy reference books?
Answer:
$1,440
Explanation:
A school raises $4,000 for its new library.
36% of the money is used to buy reference books.
Total money is used to buy reference books
36% of $4,000
= $\frac{36}{100}$ × 4000
= 1440

Question 7.
Ms. Galan spent 55% of her savings on a television that cost $550. How much money did she have in her savings before she bought the television?
Answer:
$1,000
Explanation:
Ms. Galan spent 55% of her savings on a television that cost $550.
Money she have in her savings before she bought the television
550 = 55% of her savings
550 = $\frac{55}{100}$ x
x = (550 x 100) ÷ 55
x = 1000

Question 8.
75% of a number is 354. Find the number.
Answer:
472 is the number
Explanation:
75% of x = 354
x = (354 x 100) ÷ 75
x = 472

Question 9.
Ahyoka has 250 CDs. 10% are country, 70% are pop, and the rest are hip-hop. How many CDs are hip-hop?
Answer:
50 CDs
Explanation:
Ahyoka has 250 CDs.
10% are country, 70% are pop = 70 + 10 = 80%
the rest are hip-hop = 100 – 80 = 20%
Total hip-hop CDs = 20% of 250
= $\frac{20}{100}$ × 250
= 50

Question 10.
There are 820 people at a stadium. 65% of them are adults, 20% of them are boys, and the rest are girls. How many girls are there at the stadium?
Answer:
123 girls
Explanation:
There are 820 people at a stadium.
65% of them are adults, 20% of them are boys = 65 + 20 = 55%
Rest of the girls = 100 – 85 = 15%
Number of girls at the stadium = 15% of 820
= $\frac{15}{100}$ × 820
= 123

Question 11.
Ms. Stapleton had 2,600 hens, ducks, and goats on her farm. 35% of them were hens, and 25% of them were goats. How many ducks did she have on her farm?
Answer:
Ducks 790
Explanation:
total 2,600 hens, ducks, and goats in farm
Hens = 2,600 x 35%
= (2,600 x 35)/100
= 26 x 35
= 910

Goats = 25% of 2,600
= (2600 x 25)/100
= 26 x 25
= 900

Ducks = 2600 – (Hens + Goats)
Hens + Goats = 910 + 900 = 1,810
Ducks = 2,600 – 1,810
= 790

Question 12.
There are 1,505 fruits for sale at a farmer’s market. 39% of them are apples, 28% are oranges, 13% are honeydew melons, and the rest are watermelons. How many watermelons are there?
Answer:
301 watermelons
Explanation:
There are 1,505 fruits for sale at a farmer’s market.
39% of them are apples, 28% are oranges, 13% are honeydew melons,
Total apples, oranges and honeydew melons = 39 + 28 + 13 = 80
Number of watermelons = 100 – 80 = 20%
Number of watermelons 20% of 1505
= $\frac{20}{100}$ × 1505
= 301

Question 13.
120% of a number is 45. Find the number.
Answer:
37.5
Explanation:
120% of x = 45
x = (45 x 100) ÷ 120
x = 37.5

Question 14.
250% of a number is 60. Find the number.
Answer:
24 is the number
Explanation:
250% of x = 60
x = (60 x 100) ÷ 250
x = 24

Question 15.
400% of a number is 45. Find the number.
Answer:
11.25 is the number
Explanation:
400% of x = 45
x = (45 x 100) ÷ 400
x = 11.25

Question 16.
Last month, Alex spent 40% of his salary on a laptop. He then spent 30% of it on his bills and saved the remaining $1,200. What was his salary?
Answer:
$4,000
Explanation:
He spent 70% of his salary and had $1200 left.
Let ‘x’ be his salary.
100% – 70% = 30% left.
30% of x = 1200
= $\frac{30}{100}$ x = 1200
0.3x = 1200
x = 1200 ÷ 0.3
x = 4000

Question 17.
20% of the spectators at a tennis match are women. 10% of them are girls, 30% are boys, and the remaining 3,600 spectators are men. Find the total number of spectators at the match.
Answer:
9,000 spectators
Explanation:
20% of the spectators at a tennis match are women.
10% of them are girls, 30% are boys,
Total women, boys and girls = 20 + 10 + 30 = 60%
Men spectators = 3600
The total number of spectators at the match
40 % of x = 3600
$\frac{40}{100}$ x = 3600
0.4x = 3600
x = 3600 ÷ 0.4
x = 9,000

Question 18.
Jovita made 300 greeting cards. She sold 40% of the cards, gave 85% of the remaining cards to her friends, and kept the rest of the cards for herself. How many greeting cards did she keep for herself?
$Math in Focus Grade 6 Chapters 6 Lesson 6.3 Answer Key Percent of a Quantity 7$
Answer:
27 greeting cards
Explanation:
Jovita made 300 greeting cards.
She sold 40% of the cards = 300
$\frac{40}{100}$ x 300 = 120
she sold 120 out of 300 = 300 – 120 = 180
she gave 85% of the remaining cards to her friends,
$\frac{85}{100}$ x 180
Remaining cards = 180 – 153
Total greeting cards she kept for herself = 27

Question 19.
Patrick saved $500. He received 25% of the money for his birthday, saved 30% of the remainder from his allowance, and earned the rest of it by mowing lawns. How much of his savings did he earn by mowing lawns?
Answer:
$262.50
Explanation:
Patrick saved $500.
He received 25% of the money for his birthday,
saved 30% of the remainder from his allowance = 25 + 30 = 75%
75% of 500
= $\frac{75}{100}$ x 500
= 75 x 5 = 375
Total savings he earn by mowing lawns
100 – 30 = 70%
70% of x = 375
0.7x = 375
x = 375 x 0.7
x = 262.50

Question 20.
Math Journal Michelle and Michael checked some books out of the library. 20% of the books Michelle checked out were fiction books, and 40% of the books Michael checked out were fiction books. Your friend thinks that Michael checked out more fiction books than Michelle. Explain the error in your friend’s thinking. Use an example to support your reasoning.
Answer:
The error in the assessment is that Michael checked more fiction books than Michelle.
Explanation:
We can determine who has more books only when we know how many books each person has checked out in total,
but not the proportion of fiction of books, (20% and 40%).
So, we can assume that Michael checked more fiction books than Michelle.