Hillary

Go through the Math in Focus Grade K Workbook Answer Key Chapter 19 Measurement to finish your assignments.

Math in Focus Kindergarten Chapter 19 Answer Key Measurement

Lesson 1 Comparing Weights Using Nonstandard Units

Circle the heavier thing.

Question 1.

Answer:

Explanation:
The watermelon is heavier than banana

Question 2.

Answer:

Explanation:
The rabbit is heavier than bird

Question 3

Answer:

Explanation:
The ball is heavier than a balloon

Circle the lighter thing.

Question 1.

Answer:

Explanation:
The Feather is lighter than the cap

Question 2.

Answer:

Explanation:
The Gloze is lighter than the bag

Question 3.

Answer:

Explanation:
The berry is lighter than the apple

Count and write.

Answer:

Explanation:
The owl weighs 9 blocks and the mouse weighs 2 blocks

Circle the heavier animal.

Answer:

Explanation:
The owl weighs more than the mouse

Count and write.

Answer:

Explanation:
The teddy bear weighs 8 blocks and  doll weighs 10 blocks

Circle the lighter thing.

Answer:

Explanation:
The teddy weighs lighter than the doll.

Lesson 2 Comparing Capacities

Circle the container that holds more.

Question 1.

Answer:

Explanation:
The yellow container can contains more than the pink

Question 2.

Answer:

Explanation:
The Brown container contains more than the purple.

Question 3.

Answer:

Explanation:
The bowl contains more than the glass

Circle the container that holds less.

Question 1.

Answer:

Explanation:
The bottle contains less than the bucket

Question 2.

Answer:

Explanation:
The jar contains less than the kettle

Question 3.

Answer:

Explanation:
The pack contains less than the can

Color the containers that hold the same amount.

Question 1.

Answer:

Explanation:
The 2 yellow jars contains the same quantity

Question 2.

Answer:

Explanation:
The 2 red jars contains the same quantity

Question 3.

Answer:

Explanation:
The 2 pink boxes contains the same quantity

Lesson 3 Comparing Events in Time

Which takes more time? Circle.

Question 1.

Answer:

Explanation:
Eating takes more time than drinking

Question 2.

Answer:

Explanation:
Cleaning takes more time than throwing the dust in dust bin

Which takes less time? Circle.

Question 1.

Answer:

Explanation:
Cleaning one cup takes less time than the more plates

Question 2.

Answer:

Explanation:
Buttoning the shirt takes more time than zipping a shirt.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 18 Subtraction Stories to finish your assignments.

Math in Focus Kindergarten Chapter 18 Answer Key Subtraction Stories

Lesson 1 Writing Subtraction Sentences and Representing Subtraction Stories

Count and write.

Question 1.

Answer:

Explanation:
The difference of 5 and 2 is 3
5 – 2 = 3

Question 2.

Answer:

Explanation:
The difference of 7 and 3 is 4
7 – 3 = 4

Question 3.

Answer:

Explanation:
The difference of 9 and 4 is 5
9 – 4 = 5

Count and write.

Question 1.

Answer:

Explanation:
The difference of 4 and 2 is 2
There are 4 bowls of soup out of that 2 fell down
4 – 2 = 2

Question 2.

Answer:

Explanation:
The difference of 1 and 0
There is 1 girl and not going anywhere so, 1 – 0 = 1

Question 3.

Answer:

Explanation:
The difference of 5 and 3 is 2
There are 5 bananas 3 were eaten
so, 2 are remaining
5 – 3 = 2

Question 4.

Answer:

Explanation:
The difference of 6 and 1 is 5
There are 6 apples and 1 fell down from the tree
6 – 1 = 5

Question 5.

Answer:

Explanation:
The difference of 9 and 5 is 4
There are 9 spiders 5 fell down and 4 are still remaining on the tree
9 – 5 = 4

Lesson 2 Comparing Sets

How many more? Circle. Write the number sentence.

Question 1.

Answer:

Explanation:
The difference of 6 and 5 is 1
There are 6 cars and 5 teddy
6 – 5 = 1
so, there is 1 more car than teddy

Question 2.

Answer:

Explanation:
The difference of 7 and 3 is 4
There are 7 basket balls and 3 American footballs
so, there are 4 more basket balls

Question 3.

Answer:

Explanation:
The difference of 8 and 5 is 3
There 8 shirts out of it there are only 5 shorts
so there are 3 more shirts

Question 4.

Answer:

Explanation:
The difference of 9 and 4 is 5
There are 9 milk packets and 4 milk bottles
so there are 5 more milk packets

Question 5.

Answer:

Explanation:
The difference of 10 and 3 is 7
There are 10 shoes out of it only 3 pairs of socks are there
7 shoes are more

How many more? Write the number sentence.

Question 1.

Answer:

Explanation:
The difference of 5 and 2 is 3
5 – 2 = 3
There are 3 more books than pencils

Question 2.

Answer:

Explanation:
The difference of 6 and 4 is 2
There are 2 more bats than balls

Question 3.

Answer:

Explanation:
The difference of 8 and 3 is 5
There are 5 more mushrooms than carrots

Question 4.

Answer:

Explanation:
The difference of 9 and 3 is 6
There are 6 more orange fishes than black fishes

Lesson 3 Subtraction Facts to 5

Match.

Answer:

Explanation:
The difference between the numbers are matched with the answers
3 – 1 = 2
2 – 1 = 1
4 – 1 = 3
5 – 0 = 5
1 – 1 = 0
4 – 0 = 4

Complete the number sentence.

Question 1.

Answer:

Explanation:
The difference of 5 and 4 is 1
5 – 4 = 1

Question 2.

Answer:

Explanation:
The difference of 3 and 3 is 0
3 – 3 = 0

Question 3.

Answer:

Explanation:
The difference of 4 and 2 is 2
4 – 2 = 2

Question 4.

Answer:

Explanation:
The difference of 1 and 0 is 1
1 – 0 = 1

Go through the Math in Focus Grade K Workbook Answer Key Chapter 17 Addition Stories to finish your assignments.

Math in Focus Kindergarten Chapter 17 Answer Key Addition Stories

Lesson 1 Writing Addition Sentences and Representing Addition Stories

Count and write.

Question 1.

Answer:

Explanation:
The sum of  pears are 7
4 + 3 = 7

Question 2.

Answer:

Explanation:
The sum of  balls are 6
2 + 4 = 6

Count and write.

Question 3.

Answer:

Explanation:
The sum of  pencils are 9
5 + 4 = 9

Question 4.

Answer:

Explanation:
The sum of  cars are 8
6 + 2 = 8

Question 5.

Answer:

Explanation:
The sum of  ducks are 10
3 + 7 = 10

Count and write.

Question 1.

Answer:

Explanation:
The sum of animals drinking the water and not drinking the water
3 + 1 = 4

Question 2.

Answer:

Explanation:
The sum of brown dogs and grey dogs in the park are 5
3 + 2 = 5

Question 3.

Answer:

Explanation:
The sum of  birds on the tree and the birds on the sky are 6
4 + 2 = 6

Question 4.

Answer:

Explanation:
The sum of  brown cows and black cows are 7
5 + 2 = 7

Question 5.

Answer:

Explanation:
The sum of  sleeping sheep’s and standing sheep’s are 8
6 + 2 = 8

Lesson 2 Addition Facts to 5

Fill in the missing numbers.

Question 1.

Answer:

Explanation:
When we add 0 to a number than the result is the same number.
Hence 0 is called the additive identity.
Adding zero means adding nothing in short.
The sum of 0 and 5 is 5

Question 2.

Answer:

Explanation:
The sum of 1 and 4 makes 5
1 + 4 = 5

Question 3.

Answer:

Explanation:
The sum of 2 and 3 makes 5
2 + 3 = 5

Question 4.

Answer:

Explanation:
The sum of 3 and 2 makes 5
3 + 2 = 5

Question 5.

Answer:

Explanation:
When we add 0 to a number than the result is the same number.
Hence 0 is called the additive identity.
Adding zero means adding nothing in short.
The sum of

Question 6.

Answer:

Explanation:
The sum of 5 and 0 is 5
5 + 0 = 5

Go through the Math in Focus Grade K Workbook Answer Key Chapter 12 Counting On and Counting Back to finish your assignments.

Math in Focus Kindergarten Chapter 12 Answer Key Counting On and Counting Back

Lesson 1 Counting On to 10

How many more to make 10? Count and write.

Question 1.

Answer: 4 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 6 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-6
X=4
therefore 4 more boxes are needed.
Or we can write as:
6+4=10.

Question 2.

Answer: 0 boxes
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-10
X=0
therefore 0 boxes are needed.
Or we can write as:
10+0=10.

Question 3.

Answer: 7 more are needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-3
X=7
therefore 7 more boxes are needed.
Or we can write as:
3+7=10.

Question 4.

Answer: 1 more are needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-9
X=1
therefore 1 more box is needed.
Or we can write as:
9+1=10.

How many more to make 10? Count and write.

Question 5.

Answer: 6 more are needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-4
X=6
therefore 6 more boxes are needed.
Or we can write as:
6+4=10.

Question 6.

Answer: 3 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-7
X=3
therefore 3 more boxes are needed.
Or we can write as:
7+3=10.

Question 7.

Answer: 8 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-2
X=8
therefore 8 more boxes are needed.
Or we can write as:
2+8=10.

Question 8.

Answer: 9 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-1
X=9
therefore 9 more boxes are needed.
Or we can write as:
9+1=10.

Question 9.

Answer: 5 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-5
X=5
therefore 5 more boxes are needed.
Or we can write as:
5+5=10.

Lesson 2 Counting Back Using Fingers

Color, count and write.

Question 1.

Answer:

Explanation:
Above-given 10 flowers and 10 leaves.
But in the box 5 flowers and 5 leaves are there.
5 flowers are given so I coloured 5 circles and counted the remaining circles.
The remaining circles are 5.
Now count the leaves present in the box=5.

Question 2.

Answer:

Explanation:
Above-given 10 spoons and 10 forks.
But in the box 6 spoons and 4 forks are there.
6 spoons are given so I coloured 6 circles and counted the remaining circles.
The remaining circles are 4.
Now count the forks present in the box=4.

Color, count and write.

Question 3.

Answer:

Above-given 10 apples and 10 bananas.
But in the box 3 apples and 4 bananas are there.
3 apples are given so I coloured 3 circles and counted the remaining circles.
The remaining circles are 7.
Now count the bananas present in the box=4.

Question 4.

Answer:

Explanation:
The above-given: 10 shoes and 10 umbrellas.
There are 8 shoes and we need to colour the 8 circles. And we need to count the remaining circles which are not coloured.
The umbrellas present in the box=2.

Lesson 3 Finding Differences Using Fingers

Count, write and circle.

Question 1.

How many more? ____________

How many fewer? ____________
Answer:

The total number of caps=9
The total number of hats=6
The caps are more than hats.
There are 3 caps more than hats
There are 3 hats less than caps.

Count, write and circle.

Question 2.

How many more? ____________

How many fewer? ____________
Answer:

The tortoise are more.
The total number of star fish=4
The total number of tortoise=8
The tortoise is 4 more than starfish

Starfish are fewer.
The starfish are 4 fewer than tortoise.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 9 Comparing Sets to finish your assignments.

Math in Focus Kindergarten Chapter 9 Answer Key Comparing Sets

Lesson 1 Comparing Sets of Up to 10

Count and Write.

Question 1.

Answer:

Explanation:
Counted 5, wrote the number in the given space.

Question 2.

Answer:

Explanation:
Counted 4, wrote the number in the given space.

Question 3.

Answer:

Explanation:
Counted 9, wrote the number in the given space.

Question 4.

Answer:

Explanation:
Counted 6, wrote the number in the given space.

Which has more? Color. Which has fewer? Circle.

Question 1.

Answer:

Explanation:
Colored 5 ducks which are more and circled fewer 3 cocks .

Question 2.

Answer:

Explanation:
Colored 7 bees which are more and circled fewer 4 frogs .

Question 3.

Answer:

Explanation:
Colored 5 socks which are more and circled fewer 4 caps.

What cannot be counted? Circle.

Question 1.

Answer:

Explanation:
Seashore cannot counted.

Question 2.

Answer:

Explanation:
Flour cannot counted.

Question 3.

Answer:

Explanation:
Tree leaves cannot counted.

Lesson 2 Comparing Sets of 11 to 20

Count and write. Circle the set with more.

Question 1.

Answer:

Explanation:
Counted 11, 13 and wrote. Circled the set 13 with more.

Question 2.

Answer:

Explanation:
Counted 16, 15 and wrote. Circled the set 16 with more.

Match one-to-one. Then, color the set with fewer.

Question 1.

Answer:

Explanation:
Matched one-to-one. Then, colored the set with fewer.

Question 2.

Answer:

Explanation:
Matched one-to-one. Then, colored the set with fewer.

Question 3.

Answer:

Explanation:
Matched one-to-one. Then, colored the set with fewer.

Lesson 3 Comparing Sets to Find the Difference

Color the extra cubes red. Count and write how many more.

Question 1.

Answer:

Explanation:
Colored the extra 3 cubes with red. Counted 13 and wrote.

Question 2.

Answer:

Explanation:
Colored the extra 5 cubes with red. Counted 12 and wrote.

Question 3.

Answer:

Explanation:
Colored the extra 8 cubes with red. Counted 26 and wrote.

Draw, count, and write.

Question 1.

The tower in Box A has ____2_____ fewer cubes than the tower in Box B.
Answer:

Explanation:
Drawn a tower of 3 cubes in Box A and drawn a tower of 5 cubes in Box B,
The tower in Box A has 2 fewer cubes than the tower in Box B.

Question 2.

Box C has ____3_______ more cubes than Box D.
Answer:

Explanation:
Drawn a tower of 14 cubes in Box  C and drawn a tower of 11 cubes in Box D,
The tower in Box C has 3 fewer cubes than the tower in Box D.

Lesson 4 Combining Sets

Count and circle.

Question 1.

Answer:

Explanation:
Counted 3 and 2 we circled 5.

Question 2.

Answer:

Explanation:
Counted 5 and 4 we circled 9.

Question 3.

Answer:

Explanation:
Counted 10 and 4 we circled 14.

Question 4.

Answer:

Explanation:
Counted 9 and 6 we circled 15.

Question 5.

Answer:

Explanation:
Counted 12 and 6 we circled 18.

Count, circle, and write.

Question 1.

Answer:

Explanation:
Counted 5 balloons and circled 5 balloons,
If I add 2 more balloons to 5, there will be 7 balloons altogether.

Question 2.

Answer:

Explanation:
Counted 10 balls and circled 10 balls,
If I add 2 more balls to 10 balls, there will be 12 balls altogether.

Question 3.

Answer:

Explanation:
Counted 12 cups and circled 12 cups,
If I add 5 more cups to 12 cups, there will be 17 cups altogether.

Count and write.

Question 1.

Answer:

Explanation:
2 and 1 more is 3.

Question 2.

Answer:

Explanation:
4 and 3 more is 7.

Question 3.

Answer:

Explanation:
5 and 2 more is 7.

Question 4.

Answer:

Explanation:
17 and 1 more is 18.

Question 5.

Answer:

Explanation:
10 and 5 more is 15.

Question 6.

Answer:

Explanation:
19 and 0 more is 19.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 8 Numbers to 100 to finish your assignments.

Math in Focus Kindergarten Chapter 8 Answer Key Numbers to 100

Lesson 1 Counting by 2s

Count and Write.

Answer:

Explanation:
There are 16 blocks, Count is 16.

Answer:

Explanation:
There are 10 blocks, Count is 10.

Answer:

Explanation:
There are 7 blocks, Count is 7.

Answer:

Explanation:
There are 4 blocks, Count is 4.

Lesson 2 Counting by 5s

Circle the groups of 5 ants.

Answer:

Explanation :
Circled the two(2) groups of 5 ants above.

Make the tally.

Answer:

Explanation:
Made the tally and result is 8.

Lesson 3 Counting by 10s to 100

How many? Count and circle.

Question 1.

Answer:

Explanation:
Counted and Circled 40.

Question 2.

Answer:

Explanation:
Counted and Circled 60.

Question 3.

Answer:

Explanation:
Counted and Circled 100.

Circle groups of 10. Then, count and circle.

How many?
20
30
40
Answer:

Count is 30,

Explanation:
Circled groups of 10. Then counted and circle 30.

Lesson 4 Numbers 20 to 49

Read and color.

Question 1.

Answer:

Explanation:
Read and colored 42.

Question 2.

Answer:

Explanation:
Read and colored 37.

How many? Count and Circle.

Question 1.

Answer:

Explanation:
Counted 27 and Circled 27.

Question 2.

Answer:

Explanation:
Counted 32 and Circled 32.

Question 3.

Answer:

Explanation:
Counted 40 and Circled 40.

Complete the sequence. Circle the missing number.

Question 1.

Answer:

Explanation:
Completed the sequence 20,21,22,23.
Circled the missing number 22.

Question 2.

Answer:

Explanation:
Completed the sequence 39,40,41,42.
Circled the missing number 40.

Question 3.

Answer:

Explanation:
Completed the sequence 27,28,29,30.
Circled the missing number 30.

Lesson 5 Numbers 50 to 79

How many? Count and circle.

Question 1.

Answer:

Explanation:
Counted and circled 52.

Question 2.

Answer:

Explanation:
Counted and circled 60.

Question 3.

Answer:

Explanation:
Counted and circled 76.

Which is the missing number? Color the balloon.

Question 1.

Answer:

Explanation:
Missing number is 53, Colored the balloon with blue.

Question 2.

Answer:

Explanation:
Missing number is 59, Colored the balloon with green.

Question 3.

Answer:

Explanation:
Missing number is 69, Colored the balloon with purple.

Color the least number orange. Color the greatest number blue.

Question 1.

Answer:

Explanation:
Colored the least number 69 with orange.
Colored the greatest number 77 with blue.

Question 2.

Answer:

Explanation:
Colored the least number 50 with orange.
Colored the greatest number 57 with blue.

Question 3.

Answer:

Explanation:
Colored the least number 60 with orange.
Colored the greatest number 79 with blue.

Question 4.

Answer:

Explanation:
Colored the least number 50 with orange.
Colored the greatest number 78 with blue.

Lesson 6 Numbers 80 to 100

How many? Count and circle.

Question 1.

Answer:

Explanation:
Counted 87 and circled 87.

Question 2.

Answer:

Explanation:
Counted 92 and circled 92.

Question 3.

Answer:

Explanation:
Counted 100 and circled 100.

Read and color.

Question 1.

Answer:

Explanation:
Read 84 and colored 84 cubes.

Question 2.

Answer:

Explanation:
Read 97 and colored 97 cubes.

Which is the missing number? Color the flag.

Question 1.

Answer:

Explanation:
The missing numberis 83, Colored the flag 83 with purple.

Question 2.

Answer:

Explanation:
The missing number is 90, Colored the flag 90 with blue.

Question 3.

Answer:

Explanation:
The missing number is 100, Colored the flag with Yellow.

Lesson 7 Numbers 1 to 100

What comes before? Color blue. What comes after? Color red.

Question 1.

Answer:

Explanation:
Colored the before 50 number 49 with blue.
Colored the after 50 number 51 with red.

Question 2.

Answer:

Explanation:
Colored the before 11 number 10 with blue.
Colored the after 11 number 12 with red.

Question 3.

Answer:

Explanation:
Colored the before 99 number 98 with blue.
Colored the after 99 number 100 with red.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 4 Counting and Numbers 0 to 10 to finish your assignments.

Math in Focus Kindergarten Chapter 4 Answer Key Counting and Numbers 0 to 10

Lesson 1 Composing and Decomposing 5

Count, write, and circle.

Question 1.

Answer:

Explanation:
There are 2 red squares and 2 green squares, 4 in all. So, i circled 4.

Question 2.

Answer:

Explanation:
There are 3 red squares and 2 green squares, 4 in all. So, i circled 5.

Color, count and write.

Question 1.

4 is __________ and ___________.
Answer:

Explanation:
I colored and wrote 2 blue squares and 2 yellow squares.

Question 2.

5 is __________ and ___________.
Answer:

Explanation:
I colored and wrote 2 blue squares and 3 yellow squares.

Question 3.

5 is __________ and ___________.
Answer:

Explanation:
I colored and wrote 2 blue squares and 2 yellow squares.

Lesson 2 Counting and Ordering Up to 10

Are there enough? Color.

Answer:

Explanation:
There are 4 bananas, 4 strawberries and 4 pears.
The other fruits are not enough as they are less than four each.

Draw enough . Count and write.

Answer:

Explanation:
I drew 5 apples and there are 5 ants and 5 apples.

Count and write.

Question 1.

Answer:

Explanation:
I counted and wrote the number 6 as there are 6 ants.

Question 2.

Answer:

Explanation:
I counted and wrote the number 5 as there are 5 ants.

Question 3.

Answer:

Explanation:
I counted and wrote the number 9 as there are 9 ants.

Question 4.

Answer:

Explanation:
I counted and wrote the number 5 as there are 5 ants.

Draw one more. Count and write.

Question 1.

Answer:

Explanation:
I drew 1 more apple and i counted and wrote the number 2 as there are 2 apples.

Question 2.

Answer:

Explanation:
I drew 1 more apple and i counted and wrote the number 3 as there are 3 apples.

Question 3.

Answer:

Explanation:
I drew 1 more apple and i counted and wrote the number 4 as there are 4 apples.

Question 4.

Answer:

Explanation:
I drew 1 more apple and i counted and wrote the number 5 as there are 5 apples.

Count and write.

Question 1.

Answer:

Explanation:
I counted and wrote the number 3 as there are 3 turnips.

Question 2.

Answer:

Explanation:
I counted and wrote the number 2 as there are 2 capsicums.

Question 3.

Answer:

Explanation:
I counted and wrote the number 5 as there are 5 green peas.

Question 4.

Answer:

Explanation:
I counted and wrote the number 6 as there are 6 chillies.

Draw, count and write.

Question 1.

Answer:

Explanation:
I drew 1 more carrot and i counted and wrote the number 2.

Question 2.

Answer:

Explanation:
I drew 3 more tomatoes and i counted and wrote the number 4.

Question 3.

Answer:

Explanation:
I drew 3 more potatoes and i counted and wrote the number 4.

Lesson 3 Using Your Fingers and Toes to Count On

Count and write.

Question 1.

Answer:

Explanation:
I counted and wrote 0 and 1 is 1.

Question 2.

Answer:

Explanation:
I counted and wrote 1 and 1 is 2.

Question 3.

Answer:

Explanation:
I counted and wrote 2 and 1 is 3.

Question 4.

Answer:

Explanation:
I counted and wrote 3 an d1 is 4.

Question 5.

Answer:

Explanation:
I counted and wrote 4 and 1 is 5.

Lesson 4 Same Number and More

Look and talk.

Answer:

How many more? Count and write.

Answer:

Explanation:
I counted and wrote the numbers how many more are needed for 5 people.

Count and write.

Question 1.

__________ more flowers are needed.
Answer:
2 more flowers are needed.

Question 2.

__________ more flowers are needed.
Answer:
3 more flowers are needed.

Question 3.

__________ more flowers are needed.
Answer:
4 more flowers are needed.

Lesson 5 Fewer Than

Circle.

Which group has fewer than 3?

Answer:

Explanation:
I circled the group that has fewer than 3.

Which group has fewer than 5?

Answer:

Explanation:
I circled the group that has fewer than 5.

Which group has fewer than 7?

Answer:

Explanation:
I circled the group that has fewer than 7.

Which group has fewer than 9?

Answer:

Explanation:
I circled the group that has fewer than 9.

Lesson 6 How Many in All?

Draw one more. How many are there in all?

Question 1.

Answer:

Explanation:
I drew 1 more orange and i counted and wrote the number 5.

Question 2.

Answer:

Explanation:
I drew 1 more ball and i counted and wrote the number 3.

Question 3.

Answer:

Explanation:
I drew 1 more balloon and i counted and wrote the number 4.

Circle, count and write.

Question 1.
Vicki eats 2 grapes. Circle the grapes that are left behind.

___________ grapes are left behind.
Answer:

Explanation:
4 grapes are left behind. So, i circled 4 grapes.

Question 2.
2 birds fly away. Circle the birds that stay behind.

___________ birds stay behind.
Answer:

Explanation:
8 birds stay behind. So, i circled 8 birds.

Question 3.
4 horses trot away. Circle the horses that stay behind.

____________ horses stay behind.
Answer:

Explanation:
3 horses stay behind. So, i circled 3 horses.

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Review Test to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 7 Review Test Answer Key

Concepts and Skills

Write an algebraic expression for each of the following.

Question 1.
A number that is 5 more than twice x
Answer:
2x + 5
Explanation:
Let’s take a number as variable x.
A number that is 5 more than twice x
2x+ 5.
A number that is 5 more than twice x
is written as 2x+5

Question 2.
The total cost, in dollars, of 4 pencils and 5 pens if each pencil costs w cents and each pen costs 2w cents
Answer:
4w + 10w = 14w
Explanation:
The total cost, in dollars, of 4 pencils and 5 pens
given, each pencil costs w cents and each pen costs 2w cents
pencils = w cents
4 pencils = 4w cents
pen = 2w cents
5 pens = 10w cents

Question 3.
The length of a side of a square whose perimeter is r units
Answer:
\(\frac{r}{4}\)
Explanation:
perimeter of a square = side x 4
side = perimeter / 4
perimeter is given as r
side = r/4

Question 4.
The perimeter of a rectangle whose sides are of lengths (3z + 2) units and (2z + 3) units
Answer:
(10z + 10) units
Explanation:
The perimeter of a rectangle whose sides are of lengths (3z + 2) units and (2z + 3) units
perimeter of a rectangle = 2 [(3z + 2) + (2z + 3)] units
=2 [ 5z + 5]
= 10z + 10

Evaluate each expression for the given value of the variable.

Question 5.
3(x + 4) – \(\frac{x}{2}\) when x = 2
Answer:
17
Explanation:
3(x + 4) – \(\frac{x}{2}\) when x = 2
= 3(2 + 4) – \(\frac{2}{2}\)
= [(3 x 6) – 1]
= 18 – 1 = 17

Question 6.
\(\frac{5 p+9}{2}\) + \(\frac{2 p+5}{3}\) when p = 5
Answer:
22
Explanation:
\(\frac{5 p+9}{2}\) + \(\frac{2 p+5}{3}\) when p = 5
= \(\frac{5 x 5 + 9}{2}\) + \(\frac{2 x 5 + 5}{3}\)
= \(\frac{25+9}{2}\) + \(\frac{10+5}{3}\)
= \(\frac{34}{2}\) + \(\frac{15}{3}\)
= \(\frac{(3×34)+(2×15)}{6}\)
= \(\frac{102+30}{6}\)
= \(\frac{132}{6}\)
= 22

Simplify each expression.

Question 7.
24k + 11 – 5k – 4
Answer:
19k + 7
Explanation:
24k + 11 – 5k – 4
= 19k + 7

Question 8.
10 + 13h – 6 – 4h + 9 + 12h
Answer:
13 + 21h
Explanation:
10 + 13h – 6 – 4h + 9 + 12h
= 10 – 6 + 9 + 13h – 4h + 12h
= 4 + 9 + 9h + 12h
= 13 + 21h

Expand each expression.

Question 9.
5(m + 3) + 2(m + 8)
Answer:
7m + 31
Explanation:
5(m + 3) + 2(m + 8)
= (5m + 15) + (2m + 16)
= 7m + 31

Question 10.
9(x + 2) + 4(5 + x)
Answer:
13x + 38
Explanation:
9(x + 2) + 4(5 + x)
= 9x + 18 + 20 + 4x
= 13x + 38

Factor each expression.

Question 11.
5a – 25
Answer:
5(a – 5)
Explanation:
5a – 25
Take 5 as a common factor
5(a – 5)

Question 12.
28 – 7x
Answer:
7(4 – x)
Explanation:
28 – 7x
Take 7 as a common factor
7(4 – x)

Question 13.
12z + 28 – 7z – 3
Answer:
5(z + 5)
Explanation:
12z + 28 – 7z – 3
= 5z – 25
= 5(z + 5)

State whether each pair of expressions are equivalent.

Question 14.
3(x + 5) and 5(x + 3)
Answer:
No, pair of expression is not equivalent.
Explanation:
3(x + 5) and 5(x + 3)
3x + 15 = 5x + 15

Question 15.
6y – 26 and 2(3y – 13)
Answer:
Yes, pair of expression equivalent.
Explanation:
6y – 26 and 2(3y – 13)
6y – 26 = 6y – 26

Question 16.
18 – 12p and 3(5 + 6p) + 3(2p + 1)
Answer:
No, pair of expression is not equivalent.
Explanation:
18 – 12p and 3(5 + 6p) + 3(2p + 1)
18 – 12p = 15 + 18p + 6p + 3
18 – 12p = 18 + 24p

Question 17.
15 – 5q and 5(q – 3)
Answer:
No, pair of expression is not equivalent.
Explanation:
15 – 5q and 5(q – 3)
15 – 5q = 5q – 15

Problem Solving

Solve. Show your work.

Question 18.
Juan is g years old and Eva is 2 years younger than Juan.
a) Find the sum of their ages in terms of g.
Answer:
(2g – 2) years
Explanation:
Juan is g years old
Eva is 2 years younger than Juan = (g – 2)
the sum of their ages in terms of g,
g + (g – 2)
So, (2g – 2) years

b) Find the sum of their ages in g years’ time, in terms of g.
Answer:
(4g – 2) years
Explanation:
Juan is g years old
Eva is 2 years younger than Juan = (g – 2)
the sum of their ages in g years’ time, in terms of g.

Question 19.
Parker bought 4 times as many marbles as Molly. Cole bought 5 fewer marbles than Parker. If Molly bought p marbles, how many marbles did Cole buy?
Answer:
(4p – 5) marbles.
Explanation:
Number of marbles Molly bought = p
Parker bought 4 times as many marbles as Molly = 4p
Cole bought 5 fewer marbles than Parker = (4p – 5)
Number of marbles bought by Cole = (4p  – 50

Question 20.
Andrea baked h muffins. Violet baked 8 fewer muffins than Andrea. Find the average number of muffins baked by both girls, in terms of h.
Answer:
(h – 4) muffins
Explanation:
Andrea baked h muffins.
Violet baked 8 fewer muffins than Andrea = (h – 8)
Average number of muffins baked by both girls, in terms of h
h + (h – 8) ÷ 2
= (2h – 8) ÷  2
= (h – 4)

Question 21.
A square garden has a side length that is 3 meters shorter than the length of a rectangular garden. Find the perimeter of the rectangular garden in terms of y.

Answer:
(8y + 8) meters
Explanation:
A square garden has a side length that is 3 meters shorter than the length of a rectangular garden.
side of square = perimeter/4
= 8y/4 = 2y
3 meters shorter than the length of a rectangular garden
= 2y + 3
Perimeter of a rectangle garden = 2 [ length + width]
Perimeter of a rectangle garden = 2 [ 2y + 3  + 2y + 1]
=2[4y+4]
=8y + 8

Question 22.
Mrs. Roberts sewed m shirts using 2 yards of cloth for each shirt. She also sewed (m + 2) dresses, using 5 yards of cloth for each dress.
a) How much cloth did she use altogether? Give your answer in terms of m.
Answer:
(7m + 10) yards
Explanation:
Mrs. Roberts sewed m shirts using 2 yards of cloth for each shirt.
She also sewed (m + 2) dresses, using 5 yards of cloth for each dress.
2m + 5 x (m+2) =
= 2m + 5m + 10
= 7m + 10 yards cloth used
b) If m = 7, find how much more cloth she used to sew the dresses than the shirts.
Answer:
31 yards
Explanation:
m = 7
5(m+2) – 2m
=5(7 + 2 ) – 2 x 7
= 5 x 9 – 14
= 45 – 14
= 31

Question on 23.
A glass jug can hold (6p + 8) quarts more water than a plastic container. 2 glass jugs and 2 plastic containers contain 56p quarts of water in all.
a) How much water can the plastic container hold? Give your answer in terms of p.
Answer:
(11p – 4) quarts
Explanation:
Let X = quarts the plastic container can hold
Then the jug can hold (6p+8) + X
2 jugs and 2 plastic containers = 56p quarts  ==>
2(6p + 8 + X) + 2X = 56p
12p + 16 + 2X + 2X = 56p
4X = 44p – 16
X = 11p – 4
The plastic container can hold 11p – 4 quarts of water

b) If p = 3, find how much water can 1 glass jug and 1 plastic container hold in all.
Answer:
84 quarts
Explanation:
A glass jug can hold (6p + 8) quarts

Question 24.
Mr. Lee can paint 20 chairs in t hours. He uses 3 liters of paint for every 12 chairs that he painted.
a) Find, in terms of t, the number of chairs that he can paint in 3 hours.
Answer:
\(\frac{60}{t}\) chairs
Explanation:
Mr. Lee can paint 20 chairs in t hours
let X number of chairs that he can paint in 3 hours.
20 => t
X => 3
3 x 20 = X x t
Xt = 60
X = \(\frac{60}{t}\) chairs

b) Find, in terms of t, the time taken by Mr. Lee to paint 7 chairs.
Answer:
\(\frac{7}{20}\) t hours
Explanation:
20 => t
7 => X
X x 20 = 7 x t
X = \(\frac{7}{20}\) t

c) If t = 4, find the amount of paint Mr. Lee has used after painting for 4 hours.
Answer:
5 liters
Explanation:
He uses 3 liters of paint for every 12 chairs that he painted.
Mr. Lee can paint 20 chairs in t hours
20 => t
if t  = 4
Mr. Lee can paint 20 chairs in 4 hours
He uses 3 liters of paint for every 12 chairs that he painted.
x ltrs for 20 chairs
3 => 12
x => 20
3 x 20 = x x 12
x = 60 / 12
x = 5 ltrs

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Lesson 7.3 Simplifying Algebraic Expressions to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 7 Lesson 7.3 Answer Key Simplifying Algebraic Expressions

Math in Focus Grade 6 Chapter 7 Lesson 7.3 Guided Practice Answer Key

Simplify each expression. Then state the coefficient of the variable In the expression.

Question 1.
x + x + x + x + x
Answer:
5x
Explanation:
x is the variable or constant,
add all the variables, we get 5x.
So, 5 is the coefficient of the variable x.

Question 2.
y + y + 6
Answer:
2y + 6
Explanation:
y is the variable, add all the variables
y + y + 6
2y + 6
So, 25 is the coefficient of the variable y

Question 3.
m + m + m + 5 + 4
Answer:
3m + 9
Explanation:
3 is the coefficient of the variable m,
add of the variables.
m + m + m + 5 + 4
3m+9

Question 4.
n + n + n + n + n + n + 12 – 8
Answer:
6n + 4
Explanation:
n is the variable, add all the variables at first.
n + n + n + n + n + n + 12 – 8
6n + 4
6 is the coefficient of the variable 2

Solve.

Question 5.
A square has sides of length x centimeters. Find the perimeter of the square in terms of x.

The perimeter of the square is centimeters.
Answer:
4x
Explanation:
x + x + x + x = 4x
The perimeter of the square is 4x centimeters.

Question 6.
The figure shows a trapezoid. The length of each side is given as shown. Find the perimeter of the trapezoid in terms of w.

10cm
The perimeter of the trapezoid is centimeters.
Answer:
3w + 10 cm
Explanation:
The perimeter of the trapezoid is 3w + 10 centimeters.

Hands-On Activity

Materials:

• paper
• ruler
• scissors

RECOGNIZE SIMPLIFIED EXPRESSIONS ARE EQ UIVALENT)

Work in pairs.

STEP 1: Make the following set of paper strips.
Let the length of the shortest strip be m units. Make and label 5 such strips.

Make and label 4 more strips of lengths 2m units, 3m units, 4m units, and 5m units.

STEP 2: Take one of the longer strips and place it horizontally.

STEP 3: Ask your partner to use the pieces of the shortest strips to match the length of the chosen strip in STEP 2.
Example

STEP 4: Write an algebraic expression to describe the number of short strips used, and simplify it. For example in STEP 3, write m + m + m = 3m.

STEP 5: Repeat the activity with other lengths of strips.
Activity 1:

m + m + m + m = 4m
Activity 2:

m + m + m + m + m = 5m

Math Journal How do the lengths of the strips show that the expressions are equivalent?
Answer:
We use the fraction strips to show differences between different fractions.
Explanation:
For example;
We start with halves and quarters.
Ask each student to pull out a 1/2 foot strip.
Now ask them to clear their desks of everything but the 1/4 pieces and the one 1/2 strip.
Then ask them to put down enough quarter pieces to make the same length as the half piece.
We can show the lengths of the strips are equivalent with expressions.

Complete.

Question 7.
Simplify x + 8x.
x + 8x =

Answer:
9x
Explanation:
We use the fraction strips to show differences between different fractions.

Simplify each expression.

Question 8.
3r + 2r
Answer: 5r
Explanation:
r is the variable in the given expression
3r + 2r
= r + r + r + r + r
= 5r
5 is the coefficient of the variable r.

Question 9.
5y + 6y
Answer:
11y
Explanation:
y is the variable in the given expression.
y + y + y + y + y + y +y + y + y + y + y = 11y
11 is the coefficient of the variable y.

State whether each pair of expressions are equivalent.

Question 10.
3a and a + a + a
Answer:
YES, pair of expressions are equivalent.
Explanation:
3a  can be expanded as a + a + a = 3a
a + a + a =  3a
So, the given statement is correct.

Question 11.
2h + 2h and 4h
Answer:
YES, pair of expressions are equivalent.
Explanation:
2h can be expanded as h + h
2h + 2h = 4h
h + h + h + h = 4h

Question 12.
2k + 5 and (k + k) • 5
Answer:
NO, pair of expressions are not equivalent.
Explanation:
2k + 5 and (k + k) • 5
2k + 5 is not equal to 2k.5
2k + 5 is not equal to 10k

Question 13.
6z + 4z and 10 + 2z
Answer:
NO, pair of expressions are notequivalent.
Explanation:
6z + 4z = 10z
10 + 2z is another expression
10z not equal to 10 + 2z

Question 14.
1p + 3p and 13p
Answer:
NO, pair of expressions are not equivalent.
Explanation:
1p + 3p = 4p
4p is not equal to 13p

Question 15.
3n + 2 + 4n and 2 + 7n
Answer:
YES, pair of expressions are equivalent.
Explanation:
both are equal
3n + 2 + 4n
= 3n + 4n + 2
= 7n + 2

Complete

Question 16.
Simplify 4s – s

4s – s =
Answer:
3s
Explanation:
We use the fraction strips to show differences between different fractions.

Simplify each expression.

Question 17.
12z – 7z
Answer:
5z
Explanation:
Subtract 12 from 7
12z – 7z = 5z

Question 18.
3p – 3p
Answer:
0
Explanation:
Subtracting 3p from 39 we get 0
3p – 3p = 0

State whether each pair of expressions are equivalent.

Question 19.
f – 6 and 6 – f
Answer:
NO, pair of expressions are not equivalent.
Explanation:
f- 6 is positive if f > 6
6-f is negative for the above f value.

Question 20.
5c – 5c and a – a
Answer:
YES, pair of expressions are equivalent.
Explanation:
5c – 5c = 0
a – a = 0
both are correct.

Simplify each expression.

Question 21.
(j + 3j) + 2j = + 2j
=
Answer:
6j
Explanation:
(j + 3j) + 2j
= 4j + 2j
= 6j

Question 22.
4j + 5j + 2j
Answer:
11j
Explanation:
4j + 5j + 2j
= 9j + 2j
= 11j

Question 23.
9t – 3t – 4t
Answer:
2t
Explanation:
9t – 3t – 4t
= 6t – 4t
= 2t

Question 24.
5t – t – 4t
Answer:
0
Explanation:
5t – t – 4t
= 4t – 4t = 0

Question 25.
8w – 6w + 3w
Answer:
5w
Explanation:
8w – 6w + 3w
= 2w + 3w
= 5w

Question 26.
7w + 2w – 6w
Answer:
3w
Explanation:
7w + 2w – 6w
= 9w – 6w = 3w

Complete.

Question 27.
The figure shows a quadrilateral. Find the perimeter of the quadrilateral.

6x + 6 + 2x + 2 = 6x + 2x + 6 + 2
= +
The perimeter of the quadrilateral is units.
Answer:
8x + 8 units
Explanation:
6x + 6 + 2x + 2
= 6x + 2x + 6 + 2
= 8x + 8 units
The perimeter of the quadrilateral is 8x + 8 units.

Simplify each expression.

Question 28.
4x – 3 + 3x
Answer:
7x – 3
Explanation:
4x – 3 + 3x
= 4x + 3x – 3
= 7x – 3

Question 29.
5y + 4 = 2y
Answer:
3y + 4 =0
Explanation:
5y + 4 = 2y
5y – 2y + 4
3y + 4 = 0

Question 30.
8y – 7 – 4y
Answer:
4y – 7
Explanation:
8y – 7 – 4y
subtract the variables first,
= 4y – 7

Question 31.
7z + 9 – 2z – 2
Answer:
5z + 7
Explanation:
7z + 9 – 2z – 2
Bring all the variables and coefficients to one side.
= 7z – 2z +9 – 2
= 5z + 7

Question 32.
5 + 11 z – 4 + 6z
Answer:
1 + 17z
Explanation:
5 + 11 z – 4 + 6z
Bring all the variables and coefficients to one side.
= 5 – 4 + 11 z + 6z
= 1 + 17z

Question 33.
8g + 10 – 3g + 7
Answer:
5g + 17
Explanation:
8g + 10 – 3g + 7
Bring all the variables and coefficients to one side.
=8g – 3g + 10 + 7
=5g + 17

Question 34.
12 + 6g – 5 – 4g
Answer:
7 – 2g
Explanation:
12 + 6g – 5 – 4g
Bring all the variables and coefficients to one side.
=12 – 5 + 6g – 4g
=7 – 2g

Question 35.
27 + 3r – 9 + 15r
Answer:
18 +18r
Explanation:
27 + 3r – 9 + 15r
Bring all the variables and coefficients to one side.
=27 – 9 +3r + 15r
=18 +18r

Math in Focus Course 1A Practice 7.3 Answer Key

Simplify each expression. Then state the coefficient of the variable in each expression.

Question 1.
u + u + u + u
Answer:
4u
Explanation:
Add all the variable to get the sum
u + u + u + u = 4u

Question 2.
v + v + 5 – 2
Answer:
2v + 3
Explanation:
v + v + 5 – 2
Add all the variable at first,
then subtract the coefficient.
Finally, write an algebraic expression.
= 2v + 5 – 2
= 2v + 3

Question 3.
w + w + w + w + w + w + 15 – 7
Answer:
6w + 8
Explanation:
Add all the variable at first,
then subtract the coefficient.
Finally, write an algebraic expression.
w + w + w + w + w + w + 15 – 7
= 6w + 15 – 7
= 6w + 8

Simplify each expression.

Question 4.
3p + p
Answer:
4p
Explanation:
3p + p
Expand the variables at first, then add.
= p + p + p + p
= 4p

Question 5.
4p + 5p
Answer:
9p
Explanation:
4p + 5p
Expand the variables at first, then add.
p + p + p + p + p + p + p + p + p
= 9p

Question 6.
7p – 2p
Answer:
5p
Explanation:
7p -2 p
Expand the variables at first, then subtract.
= (p + p + p + p + p + p + p) – (p + p)
= 5p

Question 7.
3p – 2p + 5p
Answer:
6p
Explanation:
3p – 2p + 5p
3p – 2p = 1p
1p + 5p = 6p

Question 8.
2p + 3p + 4p + 5p – 6p – 7p
Answer:
p
Explanation:
2p + 3p + 4p + 5p – 6p – 7p
14p – 13p = p

State whether each pair of expressions are equivalent.

Question 9.
5x and x + x + 3x
Answer:
YES, pair of expressions are equivalent.
Explanation:
x + x + 3x = 5x
So, 5x and x + x + 3x are equivalent.

Question 10.
4y + 2y + y and 5y + y
Answer:
NO, pair of expressions are not equivalent.
Explanation:
4y + 2y + y and 5y + y
4y+2y+y = 7y
5y+y=6y
7y is not equal to 6y

Question 11.
2z + 5 and z + 8 + z – 3
Answer:
YES, pair of expressions are equivalent.
Explanation:
2z + 5 and z + 8 + z – 3
2z + 5
z + 8 + z – 3 = 2z+5
both are equal

Question 12.
2w – 5 and 5 – 2w
Answer:
No, pair of expressions are not equivalent.
Explanation:
2w – 5 and 5 – 2w
2w – 5, here coefficient is negative and variable is positive.
-2w + 5, here coefficient is positive and variable is negative.

Question 13.
11u – 4u and 11 – 4 + u
Answer:
No, pair of expressions are not equivalent.
Explanation:
11u – 4u and 11 – 4 + u
11u – 4u = 7u
11 – 4 + 4 = 7 + u
7 + u is not 7u

Question 14.
3v + v and \(\frac{12v}{3}\)
Answer:
Yes, pair of expressions are equivalent.
Explanation:
3v + v and \(\frac{12v}{3}\)
3v + v = 4v
\(\frac{12v}{3}\) = 4v
4v is equal \(\frac{12v}{3}\)

Simplify each expression.

Question 15.
3x + 5 + 4x + 6
Answer:
7x + 11
Explanation:
3x + 5 + 4x + 6
Add all the variables and coefficients.
= 3x + 4x + 5 + 6
= 7x + 11

Question 16.
3x + 2x + 3x + 2
Answer:
8x + 2
Explanation:
3x + 2x + 3x + 2
Add all the variables at first,
= 8x + 2

Question 17.
17 + 4w – 12 – w
Answer:
5 + 3w
Explanation:
17 + 4w – 12 – w
= 17 -12 + 4w – w
= 5 + 3w

Question 18.
9 + 5u + 6u – 7 – 8u + 4
Answer:
6 + 3u
Explanation:
9 + 5u + 6u – 7 – 8u + 4
= 9 – 7 + 4 + 5u + 6u – 8u
= 6 + 3u

Solve.

Question 19.
A book has a length of (b + 2) inches and a width of b inches. Write a simplified expression for the perimeter of the book.

Answer:
4b + 4 inches
Explanation:
A book has a length of (b + 2) inches and a width of b inches.
Perimeter = 2(length + width)
= b + 2 + b + b + 2 + b
Add all the variables and coefficients to write an equation.
= 4b + 4 inches is the perimeter of the book.

Question 20.
The figure shows a quadrilateral. The length of each side is given as shown. Find the perimeter of the quadrilateral in terms of z.

Answer:
3z + 15 cm
Explanation:
The length of each side is given as shown.
The perimeter of the quadrilateral in terms of z.
p = z + 8 + z + 3 + z + 4
= 3z + 15 cm

Question 21.
Anne is currently h years old. Bill is currently 2h years old and Charles is currently 8 years old. Find an expression for each person’s age after h years. Then find an expression for the sum of their ages after h years.
Answer:
8 + h years
Explanation:
Anne h years
Bill is 2h years
Charles is 8 years
an expression for each person’s age after h years
Anne h + h = 2h years
Bill is 2h + h = 3h years
Charles is 8 + h years

Question 22.
There are 18 boys in a class. There are w fewer boys than girls. How many students are there in the class?
Answer:
36 – w
Explanation:
Boys  = 18
Girls = 18 – w
Total number of students = 18 + 18 – w
= 36 – w

Question 23.
A rectangular garden has a length of (y + 2) yards and a width of (4y – 1) yards. Find the perimeter of the garden in terms of y.
Answer:
10y + 2
Explanation:
A rectangular garden has a length of (y + 2) yards and a width of (4y – 1) yards.
The perimeter of the garden in terms of y.
p = y + 2 + 4y – 1 + y + 2 + 4y – 1
p = 10y + 2
the perimeter of the garden in terms of y is = 10y + 2

Question 24.
Kayla had 64b dollars. She gave \(\frac{1}{8}\) of it to Luke and spent $45. How much money did Kayla have left? Express your answer in terms of b.
Answer:
\(\frac{520b -360} {8}\)
Explanation:
Kayla had 64b dollars.
She gave \(\frac{1}{8}\) of it to Luke and spent $45.
64b- \(\frac{1}{8}\) -45
= \(\frac{64b x  8 + 8b -45 x 8} {8}\)
= \(\frac{520b – 360} {8}\)

Question 25.
A rectangle has a length of (2m + 1) units and a width of (10 – m) units. A square has sides of length \(\frac{2 m+1}{2}\) units.
a) Find the perimeter of the rectangle.
Answer:
2m + 22
Explanation:
length of (2m + 1) units and a width of (10 – m) units
the perimeter of the rectangle is
= 2m + 1 + 10 – m + 2m + 1 + 10 – m
= 2m + 22

b) Find the perimeter of the square.
Answer:
4 x  \(\frac{2 m+1}{2}\) units
Explanation:
length \(\frac{2 m+1}{2}\) units
Perimeter of a square =4 x  \(\frac{2 m+1}{2}\) units

c) Find the sum of the perimeters of the two figures if m = 6.
Answer:
26 units
Explanation:
the perimeters of the two figures if m = 6
Perimeter of a square = 4 x  \(\frac{2 m+1}{2}\) units
= 4 x  \(\frac{2 x 6+1}{2}\) units
= 4 x  \(\frac{13}{2}\) units
= 26 units
the perimeter of the rectangle is = 2m + 22 units
=2 x 9 + 22
= 18 + 22
= 40 units

d) If m – 6, the perimeter of the rectangle is greater than the perimeter of the square. Find how many units greater the rectangle’s perimeter is than the square’s perimeter.
Answer:
40 units
Explanation:
the perimeters of the two figures if m = 6
Perimeter of a square = 26 units
the perimeter of the rectangle is = 40 units

Question 26.
Math Journal Rita simplified the expression 10w – 5w + 2w in this way:

Is Rita’s answer correct? If not, explain why it is incorrect.
Answer:
Is Rita’s answer Wrong
Explanation:
In the above math journal of Rita,
she wrote the express as -5w + 2w = – 7
where as the correct express is 10w – 5w = 5w
5w + 2w = 7w

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 4 Lesson 4.1 Comparing Two Quantities to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 4 Lesson 4.1 Answer Key Comparing Two Quantities

Math in Focus Grade 6 Chapter 4 Lesson 4.1 Guided Practice Answer Key

Complete.

Question 1.
The ratio of the number of CDs to the number of CD sleeves is : .

Answer:
3 : 5
Explanation:
The number of CDs = 3
The number of sleeves = 5
the ratio of CDs = 3:5

Question 2.
Mrs. Carter buys 4 bags of apples and 7 bags of oranges. Each bag has an equal number of fruits.

The ratio of the number of apples to the number of oranges is : .
Answer:
4 : 7
Explanation:
The number of apples = 4
The number of oranges = 7
The ratio of the number of apples to the number of oranges is 4:7

Question 3.
Desiree has a cat that weighs 12 pounds and a dog that weighs 13 pounds.

a) The ratio of the weight of the cat to the weight of the dog is : .
Answer:
12 : 13
Explanation:
The weight of cat = 12lb
The weight of dog = 13lb
The ratio of the weight of the cat to the weight of the dog is =12:13

b) The ratio of the weight of the dog to the weight of the cat is : .
Answer:
13 : 12
Explanation:
The weight of cat = 12lb
The weight of dog = 13lb
The ratio of the weight of the dog to the weight of the cat is = 13:12

State whether each of the following can be expressed as a ratio.

Question 4.
6 kg and 84 kg
Answer:
yes, expressed as 1 : 14
Explanation:
The ratio of 6 kg and 84kg is expressed as
= 6 : 84
=1 : 14

Question 5.
72 ft and 2 yd
Answer:
yes, expressed as 1 : 12
Explanation:
The ratio of  72ft and 2yds
To express in ration we should convert the both the numbers in one unit( Either in feet of yards) as shown below
(2yd = 6ft)
= 6 : 72
= 1 : 12

Question 6.
3 oz and 30 in.
Answer:
yes, expressed as 1 : 6
Explanation:
The ratio of 3 oz and 30 in.
3 oz = 5in
3 oz = 5.2 in
= 5 : 30
= 1:6

Complete.

Question 7.
13 cm : 2 m = 13 cm : cm Think: 1 m = 100 cm, so 2 m = cm.
= : .
Answer:
13 : 200
Explanation:
13 cm : 2 m = 13 cm : 200 cm
Think: 1 m = 100 cm,
so 2 m = 200 cm.
= 13 : 200.

Question 8.
5 kg : 13 g = g : g Think: 1 kg = 1,000 g, so 5 kg = g.
= : .
Answer:
5000 : 13
Explanation:
5 kg : 13 g = 5000 g : 13 g
Think: 1 kg = 1,000 g,
so 5 kg = 5000 g.
5000 : 13

Question 9.
9 mL : 7 L = mL : mL Think: 1 L = 1,000 mL, so 7 L = mL.
= : .
Answer:
9 : 7000
Explanation:
9 mL : 7 L = 9 mL : 7000 mL
Think: 1 L = 1,000 mL,
so 7 L = 7000 mL.
= 9 : 7000

Question 10.
John keeps 17 angelfish and 24 guppies.

a) Find the ratio of the number of angelfish to the number of guppies.
The ratio of the number of angelfish to the number of guppies is : .
Answer:
17 : 24
Explanation:
John keeps 17 angelfish and 24 guppies

The ratio of the number of angelfish to the number of guppies is 17 : 24

b) Find the ratio of the number of guppies to the total number of fish.
Total number offish = +
=
The ratio of the number of guppies to the total number of fish is 24 : 41.
Answer:
24 : 58
Explanation:
John keeps 17 angelfish and 24 guppies
Total number offish = 17 + 41 = 58
The ratio of the number of guppies to the total number of fish is 24 : 58.

Question 11.
Alex has a string 72 centimeters long. He cuts it into two pieces. The length of the shorter piece is 31 centimeters. What is the ratio of the length of the longer piece to the total length of the string?

72 – =
The length of the longer piece is centimeters,
cm : cm = :
The ratio of the length of the longer piece to the total length of the string is : .
Answer:
41 : 72
Explanation:

72 – 31 = 41
The length of the longer piece is 41 centimeters,
31 cm : 41 cm = 31 : 41
The ratio of the length of the longer piece to the total length of the string is 41 : 72.

Question 12.
The total amount of money Pamela and Rachel saved in a week was $45. Pamela saved $13.
a) Find the amount of money Rachel saved.
Answer:
$32
Explanation:
The total amount of money Pamela and Rachel saved in a week was $45
Pamela saved $13.
$45 – $13 = $32
the amount of money Rachel saved = $32

b) Find the ratio of the total amount of money Pamela and Rachel saved to the amount of money Rachel saved.
Answer:
4 : 9
Explanation:
The total amount of money Pamela and Rachel saved in a week was $45
The amount of money Rachel saved = $32
The ration of the total amount of money Pamela and Rachel saved to the amount of money Rachel saved is 32 : 72
4 : 9  (8 x 4 = 32  and  8 x 9 = 72)

Complete. You may draw a model to help you.

Question 13.
The ratio of the number of white parrots to the number of green parrots is 7 : 8. Write a ratio to describe the number of green parrots to the total number of parrots.
Total number of parrots = + = units
The ratio of the number of green parrots to the total number of parrots is : or \(\frac{?}{?}\).
Answer:
8 : 15
Explanation:
The ratio of the number of white parrots to the number of green parrots is 7 : 8.
Total number of parrots = 7 + 8 = 15 units
The ratio of the number of green parrots to the total number of parrots is 8 : 15 or
\(\frac{8}{15}\).

Solve. You may draw a model to help you.

Question 14.
The ratio of the number of male teachers to the number of female teachers in a school is 5 : 9.
a) What fraction of the teachers are females?
Answer:
\(\frac{9}{14}\).

b) What fraction of the teachers are males?
Answer:
\(\frac{5}{14}\).
Explanation:
The ratio of the number of male teachers to the number of female teachers in a school is 5 : 9.
Total teachers = 5 + 9 = 14
fraction of male teachers = \(\frac{9}{14}\).

fraction of female teachers = \(\frac{5}{14}\)

Complete.

Question 15.
The height of a coconut tree is 48 feet and the height of a papaya tree is 12 feet.
a) How many times the height of the papaya tree is the height of the coconut tree?

The height of the coconut tree is times the height of the papaya tree.
Answer:
4ft
Explanation:
The height of a coconut tree is 48 feet and the height of a papaya tree is 12 feet.
The height of the coconut tree is 4 times the height of the papaya tree.

b) How many times the height of the coconut tree is the height of the papaya tree?

The height of the papaya tree is times the height of the coconut tree.
Answer:
\(\frac{1}{4}\).
Explanation:
The height of a coconut tree is 48 feet and the height of a papaya tree is 12 feet.
The height of the papaya tree is 1/4 times the height of the coconut tree.

Math in Focus Course 1A Practice 4.1 Answer Key

Write two ratios to compare the quantities.

Question 1.

Answer:
9 : 5
Explanation:
there are 9 sun flowers
there are 5 flower vases
the ratio of flowers and vases are 9:5

Question 2.
Catherine has 23 video game disks and Dylan has 37 video game disks.

Answer:
23 : 37
Explanation:
Catherine has 23 video game disks and Dylan has 37 video game disks.
Ratio of the both video games = 23 : 37

Question 3.
In a school, there are 8 classes in the sixth grade and 7 classes in the seventh grade. Each class has an equal number of students.

Answer:
8 : 7
Explanation:
In a school, there are 8 classes in the sixth grade and 7 classes in the seventh grade.
Each class has an equal number of students
Ratio of the students = 8 : 7

State whether each of the following can be expressed as a ratio.

Question 4.
6 cm and 60 g
Answer:
No, it can’t be expressed in ratio.
Explanation:
Both the quantities must be of same units,
here both are different in units, which can not be compared.

Question 5.
54 kg and 54 m
Answer:
No, it can’t be expressed in ratio.
Explanation:
Both the quantities must be of same units,
here both are different in units, which can not be compared.

Question 6.
12 g and 45 kg
Answer:
Yes, it can be expressed in ratio.
Explanation:
Both the quantities must be of same units.
45Kg = 45 x 1000 = 45000g
1kg = 1000g
12 : 45000

Question 7.
87 ft and 93 yd
Answer:
Yes, it can be expressed in ratio.
Explanation:
Both the quantities must be of same units.
1yd = 3ft
93 x 3  = 279 ft
87 ft : 279 ft
29 : 93

Solve. Show your work.

Question 8.
There are 123 students in a drama club. 65 of them are girls.
a) What is the ratio of the number of boys to the number of girls?
Answer:
58 : 65
Explanation:
There are 123 students in a drama club.
65 of them are girls.
number of boys 123 – 65 =58
the ratio of the number of boys to the number of girls = 58 : 65

b) What is the ratio of the number of boys to the total number of students?
Answer:
58 : 123
Explanation:
There are 123 students in a drama club.
65 of them are girls.
the number of boys 123 – 65 =58
the ratio of the number of boys to the total number of students = 58 : 123

Question 9.
There were 37 clarinet players and 150 trumpet players who tried out for a music competition.

a) Find the ratio of the number of clarinet players to the number of trumpet players.
Answer:
37 : 150
Explanation:
There were 37 clarinet players and 150 trumpet players who tried out for a music competition.
The ratio of the number of clarinet players to the number of trumpet players = 37 : 150

b) Find the ratio of the number of trumpet players to the total number of players.
Answer:
150 : 187
Explanation:
There were 37 clarinet players and 150 trumpet players who tried out for a music competition.
the total number of players = 37 + 150 = 187
the ratio of the number of trumpet players to the total number of players = 150 : 187

Question 10.
CD Carl had $43 when he entered the museum gift shop. After spending some money, he had $18 left.
a) Find the amount of money Carl spent.
Answer:
$25
Explanation:
CD Carl had $43
he had $18 left.
He spend money 43 – 18 = 25

b) Find the ratio of the amount of money Carl spent to the amount of money he had when he entered the gift shop.
Answer:
25 : 43
Explanation:
CD Carl had $43
he spend $25.
the ratio of the amount of money Carl spent to the amount of money he had 25 : 43

Question 11.
Kelvin’s monthly allowance is $42 and Mike’s monthly allowance is $63. How many times Mike’s monthly allowance is Kelvin’s monthly allowance?
Answer:
\(\frac{3}{2}\).
Explanation:
Kelvin’s monthly allowance is $42
Mike’s monthly allowance is $63
\(\frac{63}{42}\) i.e., { 21 x 2 = 42 & 21 x 3 = 63}

Question 12.
The ratio of the weight of vegetables sold to the weight of fruits sold is 45 : 144.
a) How many times the weight of vegetables sold is the weight of fruits sold?
Answer:
\(\frac{45}{144}\)

b) What fraction of the total weight of vegetables and fruits sold is the weight of vegetables sold?
Answer:
\(\frac{144}{189}\)
Explanation:
The ratio of the weight of vegetables sold to the weight of fruits sold is 45 : 144.
Total vegetables and fruits = 144 + 45 = 189
number of times the weight of vegetables sold is the weight of fruits sold
= \(\frac{45}{144}\)
fraction of the total weight of vegetables and fruits sold is the weight of vegetables sold
= \(\frac{144}{189}\)

Question 13.
The ratio of the length to the width of a rectangle is 5 : 2.
a) Express the difference between the length and the width of the rectangle as a fraction of the length of the rectangle.
Answer:
The difference is 3
Explanation:
The ratio of the length to the width of a rectangle is 5 : 2.
difference between width and length
= 5 – 2 = 3
b) Express the width of the rectangle as a fraction of the perimeter of the rectangle.
Answer:
\(\frac{1}{7}\)
Explanation:
The ratio of the length to the width of a rectangle is 5 : 2.
difference between width and length
= 5 – 2 = 3
perimeter = \(\frac{2}{14}\)
\(\frac{1}{7}\)

Math Journal Describe a situation that each ratio could represent.

Question 14.
5 : 16
Answer:
5 : 16
Number of base ball players : Number of foot ball players
Explanation:
The ratio of Baseball players and Football players are 5 : 16

Question 15.
98 : 3
Answer:
98 : 3
Number of students present : Number of students absent
Explanation:
The ratio of students present in a class are,
98 : 3

Question 16.
1,000 : 1
Answer:
Scale for maps
1000 m : 1 km
Explanation:
The ratio of scales on maps are represented as meters and kilometers.