## Math in Focus Kindergarten Workbook Answer Key Online | Math in Focus Grade K Answers

Math in Focus Kindergarten Workbook Answer Key present here is created using a unique approach. Singapore Math in Focus Grade K Answers is designed on basis of powerful visual models, engaging hands-on activities. With Consistent Practice using Math in Focus Answer Key for Kindergarten, one can develop critical thinking skills as well as build confidence needed for achieving good grades.  Math in Focus Grade K Workbook Answer Key for 1A & 1B will ensure you master the concepts and apply mathematics to real-life situations.

## Singapore Math in Focus Kindergarten Answer Key | Math in Focus Grade K Workbook 1A & 1B Answers

Explore new concepts of Kindergarten using the Math in Focus Kindergarten Answer Key and enhance your fundamentals. Comprehensive and easy-to-use resources for both the parts 1A & 1 B will help you develop a foundational understanding. A Consistent and Clear Teaching Path will foster your focus on new content as well as encourage mathematical thinking.  Access the Singapore Homeschool Math Grade K Workbook Answer Key PDFs of all chapters through the quick links below and ace up your preparation like never before.

### Math in Focus Kindergarten Workbook A Part 1 Answers Key

Chapter 1 Numbers to 5

• Lesson 1 All About 1 and 2
• Lesson 2 Finding Matches
• Lesson 3 Not the Same but Different: All About 3
• Lesson 4 Why Is This Different? All About 4
• Lesson 5 All About 5
• Lesson 6 Spotting Small Differences

Chapter 2 Numbers to 10

• Lesson 1 All About 6
• Lesson 2 All About 7
• Lesson 3 All About 8
• Lesson 4 Numbers 0 to 9
• Lesson 5 Pairing Sets with Numbers
• Lesson 6 Pairing One-to-One

### Math in Focus Grade K Workbook A Part 2 Answers Key

Chapter 3 Order by Size, Length, or Weight

• Lesson 1 Ordering Things by Size
• Lesson 2 Comparing Sizes
• Lesson 3 Ordering Things by Length
• Lesson 4 Ordering Things by Weight

Chapter 4 Counting and Numbers 0 to 10

• Lesson 1 Composing and Decomposing 5
• Lesson 2 Counting and Ordering Up to 10
• Lesson 3 Using Your Fingers and Toes to Count On
• Lesson 4 Same Number and More
• Lesson 5 Fewer Than
• Lesson 6 How Many in All?

Chapter 5 Size and Position

• Lesson 1 Big and Small Things
• Lesson 2 Does It Fit?
• Lesson 3 Positions
• Lesson 4 ‘Before’ and ‘After’

Chapter 6 Numbers 0 to 20

• Lesson 1 All About 10
• Lesson 2 Numbers 10 to 12
• Lesson 3 Numbers 13 to 16
• Lesson 4 Numbers 17 to 20
• Lesson 5 Compare and Order

### Math in Focus Kindergarten Workbook B Part 1 Answers Key

Chapter 7 Solid and Flat Shapes

• Lesson 1 Solid Shapes
• Lesson 2 Flat Shapes in Solid Shapes
• Lesson 3 Flat Shapes
• Lesson 4 Flat Shape Pictures
• Lesson 5 Shape Patterns

Chapter 8 Numbers to 100

• Lesson 1 Counting by 2s
• Lesson 2 Counting by 5s
• Lesson 3 Counting by 10s to 100
• Lesson 4 Numbers 20 to 49
• Lesson 5 Numbers 50 to 79
• Lesson 6 Numbers 80 to 100
• Lesson 7 Numbers 1 to 100

Chapter 9 Comparing Sets

• Lesson 1 Comparing Sets of Up to 10
• Lesson 2 Comparing Sets of 11 to 20
• Lesson 3 Comparing Sets to Find the Difference
• Lesson 4 Combining Sets

Chapter 10 Ordinal Numbers

• Lesson 1 Sequencing Events
• Lesson 2 Physical Position
• Lesson 3 Showing Your Preferences

Chapter 11 Calendar Patterns

• Lesson 1 Days of the Week
• Lesson 2 Months of the Year

Chapter 12 Counting On and Counting Back

• Lesson 1 Counting On to 10
• Lesson 2 Counting Back Using Fingers
• Lesson 3 Finding Differences Using Fingers

Chapter 13 Patterns

• Lesson 1 Repeating Patterns

Chapter 14 Number Facts

• Lesson 1 Number Facts to 10
• Lesson 2 Combining Sets
• Lesson 3 Composing and Decomposing Numbers to 20
• Lesson 4 Counting On

### Math in Focus Grade K Workbook B Part 2 Answers Key

Chapter 15 Length and Height

• Lesson 1 Comparing Lengths
• Lesson 2 Comparing Lengths Using Nonstandard Units
• Lesson 3 Comparing Heights Using Nonstandard Units

Chapter 16 Classifying and Sorting

• Lesson 1 Classifying Things by One Attribute
• Lesson 2 Classifying and Sorting Things by Two Attributes

Chapter 17 Addition Stories

• Lesson 1 Writing Addition Sentences and Representing Addition Stories
• Lesson 2 Addition Facts to 5

Chapter 18 Subtraction Stories

• Lesson 1 Writing Subtraction Sentences and Representing Subtraction Stories
• Lesson 2 Comparing Sets
• Lesson 3 Subtraction Facts to 5

Chapter 19 Measurement

• Lesson 1 Comparing Weights Using Nonstandard Units
• Lesson 2 Comparing Capacities
• Lesson 3 Comparing Events in Time

Chapter 20 Money

• Lesson 1 Coin Values
• Lesson 2 Counting Coins

### Features of Math in Focus Homeschool Kindergarten Workbook Answer Key PDF

Below are some of the key features of Math in Focus Grade K Workbook Answers given by us. They are along the lines

• The Pictorial Abstract Approach i.e. hands-on diagrams, models, symbols, and manipulatives used in explaining the concepts makes it easy for students to have a deeper conceptual understanding.
•  All the questions in the Homeschool Singapore Math Grade K Textbook are explained step by step so that you can grasp the concepts easily.
• Math in Focus Grade K Workbook 1A & 1B Answers provided here will guide students in acquiring and applying concepts and skills to real-world problems too.
• Kindergarten Math in Focus Workbook Answer Key PDF available follows the consistent k-8 pedagogical approach and is in accordance with the Latest Singapore Math Curriculum.
• Interactive exercises and fun learning activities used in the Singapore Math Grade K Workbook Answer Key will ensure the overall growth of a student.

### Final Words

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## Math in Focus Kindergarten Chapter 20 Answer Key Money

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

## Math in Focus Kindergarten Chapter 20 Answer Key Money

Lesson 1 Coin Values

Match.

Explanation:
1 quarter dollar is equal to 25 cents
1 dime is equal to 10 cents
1 nickel is equal to 5 cents
1 penny is equal to 1 cent

Lesson 2 Counting Coins

How many pennies do you need? Color.

Question 1.

Explanation:
The cost of the toy airplane is 6 cents
so, colored 6 cents

Question 2.

Explanation:
The cost of the toys are 6 + 2 = 8
so, colored the 8 cents

Question 3.

Explanation:
The cost of the toys are 3 + 5 = 8 cents
so, colored 8 cents

Question 4.

Explanation:
The cost of the toys are 2 + 4 + 3 = 9 cents
so, colored 9 cents

How much is needed? Circle the purse.

Question 1.

Explanation:
The cost of the toy house is 9 cents
5 + 4 = 9 cents
so, colored the first purse

Question 2.

Explanation:
The cost of the toys are 4 cents and 2 cents
4 + 2 = 6 and also
5 + 1 = 6
so circled 6 cents purse

## Math in Focus Kindergarten Chapter 19 Answer Key Measurement

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.

Explanation:
The watermelon is heavier than banana

Question 2.

Explanation:
The rabbit is heavier than bird

Question 3

Explanation:
The ball is heavier than a balloon

Circle the lighter thing.

Question 1.

Explanation:
The Feather is lighter than the cap

Question 2.

Explanation:
The Gloze is lighter than the bag

Question 3.

Explanation:
The berry is lighter than the apple

Count and write.

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

Circle the heavier animal.

Explanation:
The owl weighs more than the mouse

Count and write.

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

Circle the lighter thing.

Explanation:
The teddy weighs lighter than the doll.

Lesson 2 Comparing Capacities

Circle the container that holds more.

Question 1.

Explanation:
The yellow container can contains more than the pink

Question 2.

Explanation:
The Brown container contains more than the purple.

Question 3.

Explanation:
The bowl contains more than the glass

Circle the container that holds less.

Question 1.

Explanation:
The bottle contains less than the bucket

Question 2.

Explanation:
The jar contains less than the kettle

Question 3.

Explanation:
The pack contains less than the can

Color the containers that hold the same amount.

Question 1.

Explanation:
The 2 yellow jars contains the same quantity

Question 2.

Explanation:
The 2 red jars contains the same quantity

Question 3.

Explanation:
The 2 pink boxes contains the same quantity

Lesson 3 Comparing Events in Time

Which takes more time? Circle.

Question 1.

Explanation:
Eating takes more time than drinking

Question 2.

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

Which takes less time? Circle.

Question 1.

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

Question 2.

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

## Math in Focus Kindergarten Chapter 9 Answer Key Comparing Sets

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.

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

Question 2.

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

Question 3.

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

Question 4.

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

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

Question 1.

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

Question 2.

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

Question 3.

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

What cannot be counted? Circle.

Question 1.

Explanation:
Seashore cannot counted.

Question 2.

Explanation:
Flour cannot counted.

Question 3.

Explanation:
Tree leaves cannot counted.

Lesson 2 Comparing Sets of 11 to 20

Count and write. Circle the set with more.

Question 1.

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

Question 2.

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

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

Question 1.

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

Question 2.

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

Question 3.

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.

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

Question 2.

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

Question 3.

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.

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.

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.

Explanation:
Counted 3 and 2 we circled 5.

Question 2.

Explanation:
Counted 5 and 4 we circled 9.

Question 3.

Explanation:
Counted 10 and 4 we circled 14.

Question 4.

Explanation:
Counted 9 and 6 we circled 15.

Question 5.

Explanation:
Counted 12 and 6 we circled 18.

Count, circle, and write.

Question 1.

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

Question 2.

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.

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.

Explanation:
2 and 1 more is 3.

Question 2.

Explanation:
4 and 3 more is 7.

Question 3.

Explanation:
5 and 2 more is 7.

Question 4.

Explanation:
17 and 1 more is 18.

Question 5.

Explanation:
10 and 5 more is 15.

Question 6.

Explanation:
19 and 0 more is 19.

## Math in Focus Kindergarten Chapter 8 Answer Key Numbers to 100

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.

Explanation:
There are 16 blocks, Count is 16.

Explanation:
There are 10 blocks, Count is 10.

Explanation:
There are 7 blocks, Count is 7.

Explanation:
There are 4 blocks, Count is 4.

Lesson 2 Counting by 5s

Circle the groups of 5 ants.

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

Make the tally.

Explanation:
Made the tally and result is 8.

Lesson 3 Counting by 10s to 100

How many? Count and circle.

Question 1.

Explanation:
Counted and Circled 40.

Question 2.

Explanation:
Counted and Circled 60.

Question 3.

Explanation:
Counted and Circled 100.

Circle groups of 10. Then, count and circle.

How many?
20
30
40

Count is 30,

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

Lesson 4 Numbers 20 to 49

Question 1.

Explanation:
Read and colored 42.

Question 2.

Explanation:
Read and colored 37.

How many? Count and Circle.

Question 1.

Explanation:
Counted 27 and Circled 27.

Question 2.

Explanation:
Counted 32 and Circled 32.

Question 3.

Explanation:
Counted 40 and Circled 40.

Complete the sequence. Circle the missing number.

Question 1.

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

Question 2.

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

Question 3.

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.

Explanation:
Counted and circled 52.

Question 2.

Explanation:
Counted and circled 60.

Question 3.

Explanation:
Counted and circled 76.

Which is the missing number? Color the balloon.

Question 1.

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

Question 2.

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

Question 3.

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

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

Question 1.

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

Question 2.

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

Question 3.

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

Question 4.

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.

Explanation:
Counted 87 and circled 87.

Question 2.

Explanation:
Counted 92 and circled 92.

Question 3.

Explanation:
Counted 100 and circled 100.

Question 1.

Explanation:
Read 84 and colored 84 cubes.

Question 2.

Explanation:
Read 97 and colored 97 cubes.

Which is the missing number? Color the flag.

Question 1.

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

Question 2.

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

Question 3.

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.

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

Question 2.

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

Question 3.

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

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

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.

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

Question 2.

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 ___________.

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

Question 2.

5 is __________ and ___________.

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

Question 3.

5 is __________ and ___________.

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

Lesson 2 Counting and Ordering Up to 10

Are there enough? Color.

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.

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

Count and write.

Question 1.

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

Question 2.

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

Question 3.

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

Question 4.

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

Draw one more. Count and write.

Question 1.

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

Question 2.

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

Question 3.

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

Question 4.

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

Count and write.

Question 1.

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

Question 2.

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

Question 3.

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

Question 4.

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

Draw, count and write.

Question 1.

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

Question 2.

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

Question 3.

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.

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

Question 2.

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

Question 3.

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

Question 4.

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

Question 5.

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

Lesson 4 Same Number and More

Look and talk.

How many more? Count and write.

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

Count and write.

Question 1.

__________ more flowers are needed.
2 more flowers are needed.

Question 2.

__________ more flowers are needed.
3 more flowers are needed.

Question 3.

__________ more flowers are needed.
4 more flowers are needed.

Lesson 5 Fewer Than

Circle.

Which group has fewer than 3?

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

Which group has fewer than 5?

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

Which group has fewer than 7?

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

Which group has fewer than 9?

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.

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

Question 2.

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

Question 3.

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.

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.

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.

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

## Math in Focus Grade 6 Chapter 5 Lesson 5.1 Answer Key Rates and Unit Rates

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 5 Lesson 5.1 Rates and Unit Rates to finish your assignments.

## Math in Focus Grade 6 Course 1 A Chapter 5 Lesson 5.1 Answer Key Rates and Unit Rates

### Math in Focus Grade 6 Chapter 5 Lesson 5.1 Guided Practice Answer Key

State whether each statement is expressed as a unit rate.

Question 1.
A monkey plucked 4 coconuts per minute.
yes, it can be expressed in unit ratio.
Explanation:
Statement is expressed as a unit rate.
per minute is unit

Question 2.
Mary paid $2 for a bottle of orange juice. Answer: Yes, it can be expressed in unit ratio. Explanation:$2 for a bottle of orange juice.
$is unit per bottle juice. Question 3. A basketball team scored 294 points in 6 games. Answer: yes, it can be expressed in unit ratio. Explanation: points are the units for games Question 4. Douglas reads 3 books in a week. Answer: Yes, it can be expressed in unit ratio. Explanation: Week is unit for reading a book. Solve. Question 5. A photocopy machine can print 405 copies in 9 minutes. What is the rate at which the machine prints the copies? Answer: 45 copies per min Explanation: Question 6. A sports center buys 1.25 acres of land for a new swimming complex. What is the cost per acre if the sports center pays$100,000 for the land?
Cost per acre = Total cost ÷ Total number of acres
= $100,000 ÷ =$$$\frac{100,000}{?}$$
= $$$\frac{?}{?}$$ =$
The unit cost of the piece of land is $per acre. Answer:$ 80,000 per acre.
Explanation:
Cost per acre = Total cost ÷ Total number of acres
= $100,000 ÷ 1.25 =$$$\frac{100,000}{1.25}$$
= $$$\frac{1,000,000}{125}$$ =$ 80,000
The unit cost of the piece of land is $80000 per acre. Question 7. A few years ago, when the fuel tank in Sally’s car was completely empty, she paid$63 to fill the tank with 22.5 gallons of gasoline. What was the cost per gallon?
Cost per gallon = Cost of gasoline ÷ Volume of gasoline filled
=$÷ =$
The unit cost of the gasoline was $per gallon. Answer:$2.8
Explanation:
Cost per gallon = Cost of gasoline ÷ Volume of gasoline filled
=$63 ÷ 22.5 =$ 2.8
The unit cost of the gasoline was $2.8 per gallon. Question 8. The table shows the costs of some food items Billy bought from a supermarket. Answer: Which type of food costs the most per pound? Cost of potatoes per pound = Cost of potatoes ÷ Weight of potatoes =$ ÷
= $The unit cost of the potatoes is$ per pound.
Cost of carrots per pound = Cost of carrots ÷ Weight of carrots
= $÷ =$
The unit cost of the carrots is $per pound. Cost of onions per pound = Cost of onions ÷ Weight of onions =$ ÷
= $The unit cost of the onions is$ per pound.
Comparing the unit costs of the food items, the unit cost of the is the greatest.
Unit cost of < Unit cost of < Unit cost of
$<$ < $So, the cost the most per pound. Answer:$1.25 cost the most per pound.
Explanation:
Cost of potatoes per pound = Cost of potatoes ÷ Weight of potatoes
= $4 ÷ 5 =$ 0.8
The unit cost of the potatoes is $0.8 per pound. Cost of carrots per pound = Cost of carrots ÷ Weight of carrots =$3 ÷ 5
= $0.6 The unit cost of the carrots is$ 0.6 per pound.
Cost of onions per pound = Cost of onions ÷ Weight of onions
= $2.5 ÷ 2 =$ 1.25
The unit cost of the onions is $1.25 per pound. Comparing the unit costs of the food items, the unit cost of the 1.25 is the greatest. Unit cost of Carrot < Unit cost of Potatoes < Unit cost of Onions$0.6 < $0.8 <$1.25
So, the $1.25 cost the most per pound. Question 9. A truck traveled a distance of 280 kilometers in 4 hours. Find the speed of the truck. Method 1 The speed of the truck is 70kilometers per hour. Method 2 Speed of truck = $$\frac{\text { Distance }}{\text { Time }}$$ = $$\frac{?}{?}$$ = km/h The speed of the truck is kilometers per hour. Answer: 70 kilometers per hour. Explanation: Speed of truck = $$\frac{\text { Distance }}{\text { Time }}$$ = $$\frac{280}{4}$$ = 70 km/h The speed of the truck is 70 kilometers per hour. Question 10. A car travels $$\frac{1}{4}$$ kilometer in $$\frac{1}{2}$$ minute. Find the speed of the car in kilometers per minute. Answer: $$\frac{1}{2}$$ kilometers per minute. Explanation: Speed of car = $$\frac{\text { Distance }}{\text { Time }}$$ Speed of car = $$\frac{1}{4}$$ ÷ $$\frac{1}{2}$$ = $$\frac{1}{4}$$ X $$\frac{2}{1}$$ = $$\frac{1}{2}$$ kilometers per minute. ### Math in Focus Course 1A Practice 5.1 Answer Key Solve. Show your work. Question 1. A machine can print 300 T-shirts in 10 minutes. How many T-shirts can the machine print in 1 minute? Answer: 30 T-shirts Explanation: A machine can print 300 T-shirts in 10 minutes. Number of T-shirts can the machine print in 1 minute = $$\frac{300}{10}$$ = 30 T-shirts can the machine print in 1 minute Question 2. Alisa types 900 words in 20 minutes. What is her typing speed in words per minute? Answer: 45 words per minute Explanation: Alisa types 900 words in 20 minutes. Her typing speed in words per minute is, = $$\frac{900}{20}$$ = 45 words per minute Question 3. A 2-liter bottle is filled completely with water from a faucet in 10 seconds. How much water is filled into the bottle each second? Answer: 200 ml bottle each second Explanation: A 2-liter bottle is filled completely with water from a faucet in 10 seconds. water is filled into the bottle each second = $$\frac{2000}{10}$$ = 200 ml bottle each second Question 4. Bill is paid$200 for 5 days of work. How much is he paid per day?
$40 per day Explanation; Bill is paid$200 for 5 days of work.
Total amount he paid per day
= $$\frac{200}{5}$$
= $40 per day Question 5. Janice swims 450 meters in 5 minutes. Find her swimming speed in meters per minute. Answer: 90 meters per minute. Explanation: Janice swims 450 meters in 5 minutes. Her swimming speed in meters per minute. = $$\frac{450}{5}$$ = 90 meters per minute. Question 6. A garden snail moves $$\frac{1}{6}$$ foot in $$\frac{1}{3}$$ hour. Find the speed of the snail in feet per hour. Answer: $$\frac{1}{2}$$ feet per hour Explanation: A garden snail moves $$\frac{1}{6}$$ foot in $$\frac{1}{3}$$ hour. The speed of the snail in feet per hour. $$\frac{1}{6}$$ ÷ $$\frac{1}{3}$$ = $$\frac{1}{6}$$ X $$\frac{3}{1}$$ = $$\frac{1}{2}$$ feet per hour Question 7. Math Journal A plumber pays$3.60 for 60 centimeters of pipe. Explain how the plumber can use the unit cost of the pipe to find the cost of buying 100 meters of the same kind of pipe. Show the calculations the plumber needs to make.
The cost of 100 meters pipe = $600 Explanation: A plumber pays$3.60 for 60 centimeters of pipe.
1 cm pipe = 3.60 ÷ 60
= 0.6 cm
1m = 100 cm
S0, 0.6 cm = 600

Question 8.
Rovan can make 48 tarts per hour. Copy and complete the table.

a) At this rate, how many tarts can Rovan make in 6 hours?
288 Tarts
Explanation:
From the above given information,
Number of tarts Rovan can make in 6 hours
6 x 48 = 288 tarts

b) At this rate, how long will she take to make 120 tarts?
2.5 hours
Explanation:
From the above given information,
Number of hours she take to make tarts = 120 ÷ 48
= 2.5 hours

Question 9.
A sprinkler system is designed to water $$\frac{5}{8}$$ acres of land in $$\frac{1}{4}$$ hour. How many acres of land can it water in 1 hour?
$$\frac{5}{2}$$ per hour
Explanation:
A sprinkler system is designed to water $$\frac{5}{8}$$ acres of land in $$\frac{1}{4}$$ hour. Total acres of land can it water in 1 hour?
= $$\frac{5}{8}$$ ÷ $$\frac{1}{4}$$
= $$\frac{5}{8}$$ X $$\frac{4}{1}$$
= $$\frac{20}{8}$$
= $$\frac{5}{2}$$

Question 10.
The table shows the costs of three types of meat John bought at a supermarket. Copy and complete the table.

Which type of meat costs the least per pound?
Chicken.
Explanation:

From the above table Chicken costs the least amount per pound.

Question 11.
Math Journal The table shows the data about distances and times for three sprinters.

Who is the fastest sprinter? Justify your answer.
Smith is the fastest sprinter
Explanation:

Question 12.
A supermarket sells the three brands of rice shown in the table below.

Raimondo wants to buy 30 kilograms of rice.
a) Which brand of rice should he buy to get the best deal, assuming that all three brands are of the same quality?
Brand A
Explanation:

b) How much will he save if he buys the cheapest brand of rice as compared to the most expensive one?
$306 Explanation: Cheapest brand price =$72
Most expensive brand price = $378 378 – 72 = 306 ## Math in Focus Grade 6 Chapter 4 Lesson 4.2 Answer Key Equivalent Ratios Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 4 Lesson 4.2 Equivalent Ratios to finish your assignments. ## Math in Focus Grade 6 Course 1 A Chapter 4 Lesson 4.2 Answer Key Equivalent Ratios ### Math in Focus Grade 6 Chapter 4 Lesson 4.2 Guided Practice Answer Key Complete. Question 1. The ratio of the number of pencils to the number of erasers is : . Answer: 1 : 2 Explanation: The ratio of the number of pencils to the number of erasers is 10 : 20 = 1 : 2 Question 2. The ratio of the number of groups of pencils to the number of groups of erasers is : . Answer: 1 : 2 Explanation: The ratio of the number of groups of pencils to the number of groups of erasers is 5 : 10 = 1 : 2 Question 3. The ratio of the number of groups of pencils to the number of groups of erasers is : . Answer: 1 : 2 Explanation: The ratio of the number of groups of pencils to the number of groups of erasers is = 1 : 2 Question 4. The ratio : , : , and : are equivalent ratios. Answer: 1 : 2 Explanation: The ratio 10 : 20, 5 : 10, and 1:2 are equivalent ratios. Question 5. Express the ratio 12 : 64 in simplest form. Answer: 3 : 16 Explanation: the ratio 12 : 64 in simplest form. Question 6. Express the ratio 7 kg : 21 g in simplest form. 7 kg = g 7 kg : 21 g = g : g = ÷ : ÷ = : Answer: 1000 : 3 Explanation: 7 kg = 7000 g 7 kg : 21 g = 7000 g : 21 g = 7000 ÷ 7 : 21 ÷ 7 = 1000 : 3 State whether each pair of ratios are equivalent. Question 7. 7 : 8 and 8 : 7 Answer: NO, pair of ratios are not equivalent. Explanation: 7 : 8 and 8 : 7 are not equivalent Question 8. 5 : 9 and 15 : 27 Answer: YES, pair of ratios are equivalent Explanation: 5 : 9 and 15 : 27 5 : 9 and 15 ÷ 3 : 27 ÷ 3 5 : 9 and 5 : 9 5 : 9 and 15 : 27 are equivalent Question 9. 12 : 13 and 24 : 39 Answer: NO, pair of ratios are not equivalent. Explanation: 12 : 13 and 24 : 39 For and 12, 24 common factor is 2, where as 13 and 39 has common factor 13 . 12 : 13 and 24 : 39 are not equivalent ratios. Question 10. 4 : 24 and 8 : 48 Answer: YES, pair of ratios are equivalent. Explanation: 4 : 24 and 8 : 48 4 : 24 and 8 ÷ 2 : 48 ÷ 2 4 : 24 and 8 : 48 are equivalent ratios. Complete. Question 11. Use multiplication to find three ratios equivalent to 7 : 8. Answer: Explanation: Question 12. Use division to find all the whole number ratios that are equivalent to 24 : 96. Answer: 24 : 96 Explanation: 24 ÷ 2 : 96 ÷ 2 => 12 : 48 24 ÷ 3 : 96 ÷ 3 => 8 : 32 24 ÷ 4 : 96 ÷ 4 => 6 : 24 24 ÷ 6 : 96 ÷ 6 => 4 : 16 24 ÷ 8 : 96 ÷ 8 => 3 : 12 Find the missing term in each pair of equivalent ratios. Question 13. Answer: 30 : 35 Explanation: 6 : 7 multiply both the numbers with 5 Question 14. Answer: 4 : 6 Explanation: 4 : 6 multiply both the numbers with 7 Question 15. 48 : 64 = : 8 Answer: 6 Explanation: 48 : 64 divided both the numbers with 8 Question 16. 4 : 9 = 36 : Answer: 81 Explanation: 4 : 9 multiply both the numbers with 9 Solve. Question 17. Selena and Drew each has a summer job. The table shows the amount of money they earn, based on the number of hours they work. a) Express the ratio of Selena’s earnings to Drew’s earnings in simplest form. Answer: 31 : 33 Explanation: Selena and Drew each has a summer job. for 1 day Selena earns$31
for 1 day Drew earns $33 ratio of Selena’s earnings to Drew’s earnings = 31 : 33 b) If Selena works 4 days, she will earn$.
If Selena works 30 days, she will earn $. Answer:$930
Explanation:
If Selena works 4 days, she will earn $124. for 1 day Selena earns$31
for 4 days = 31 x 4 = 124
If Selena works 30 days, she will earn $930. 31 x 30 = 930 c) If Drew works 4 days, he will earn$.
If Drew works 30 days, he will earn $. Answer: If Drew works 4 days, he will earn$132.
If Drew works 30 days, he will earn $990. Explanation: for 1 day Drew earns$33
for 4 days = 33 x4 = 132
for 30 days = 30 x 33 = 990

Question 18.
A school organized a paper recycling competition. The table shows the amount of oil and the amount of water saved by recycling paper.

a) How many gallons of water will be saved if 1 ton of paper is recycled?
7,000gal
Explanation:
for 2 tons the amount of water saved is 14,000
So, for 1 ton 14000 ÷ 2 = 7000

b) Express the ratio of the amount of oil saved to the amount of water saved in simplest form.
19 : 350
Explanation:
Weight of paper recycled for 1 ton =
Amount of oil saved : Amount of water saved
380 : 7000
= 19 : 350

c) How many gallons of oil will be saved if 2 tons of paper are recycled?
760gal
Explanation:
for 1 ton of paper recycle need 380gal of oil saved.
for 2 tons oil saved = 380 x 2 = 760

d) How many gallons of water will be saved if 3 tons of paper are recycled?
21,000gal
Explanation:
for 1 ton of paper recycle need 7,000gal of water saved.
for 2 tons water saved = 7000 x 3 = 21,000

e) How many gallons of oil and water will be saved if 4 tons of paper are recycled?

Explanation:
for 1 ton of paper recycle need 7,000gal of water saved.
for 4 tons water saved = 7000 x 4 = 28,000gal
for 1 ton of paper recycle need 380gal of oil saved.
for 4 tons oil saved = 380 x 4 = 1520gal

### Math in Focus Course 1A Practice 4.2 Answer Key

Express each ratio in simplest form.

Question 1.
13 : 39
1 : 3
Explanation:
13 : 39
common factor for both the numbers is 13
so, 1 : 3

Question 2.
16 : 40
2 : 5
Explanation:
16 : 40
common factor for both the numbers is 8
so, 2 : 5

Question 3.
25 : 15
5 : 3
Explanation:
25 : 15
common factor for both the numbers is 5
so, 5 : 3

Question 4.
56 : 21
8 : 3
Explanation:
56 : 21
common factor for both the numbers is 7
so, 8 : 3

Question 5.
30 : 54
5 : 9
Explanation:
30 : 54
common factor for both the numbers is 6
so, 5 : 9

Question 6.
72 : 48
8 : 6
Explanation:
72 : 38
common factor for both the numbers is 8
so, 8 : 6

Question 7.
26 cm : 4 m
13cm : 200cm
Explanation:
26cm : 4m
convert m in cm
1m = 100 cm
4m = 400cm
26cm : 400cm
common factor for both the numbers is 2
so, 13 : 200

Question 8.
9 kg : 36 g
250g : 1g
Explanation:
9kg : 36g
convert kg to g
1kg = 100o g
9kg = 9000g
250g : 1g
common factor for both the numbers is 9
so, 250 : 1

Question 9.
35 min : 2 h
7min : 24min
Explanation:
35m : 2h
convert hr in min
1hr = 60min
2hr = 120min
35min : 120min
common factor for both the numbers is 5
so, 7 : 24

State whether each pair of ratios are equivalent.

Question 10.
11 : 17 and 17 : 11
No, pair of ratios are not equal
Explanation:
11 : 17 and 17 : 11
the given numbers are not equivalent to their ratios.

Question 11.
7 : 11 and 21 : 33
YES, pair of ratios are equal.
Explanation:
7 : 11 and 21 : 33
The common factor for both the numbers is 3
So, both are equivalent.

Question 12.
15 : 35 and 25 : 45
NO, pair of ratios are not equal.
Explanation:
15 : 35 and 25 : 45
3 : 7  and 5 : 9
The common factor for both the numbers is 5
So, both are not equivalent.

Question 13.
15 : 20 and 20 : 25
NO, pair of ratios are not equal.
Explanation:
15 : 20 and 20 : 25
3 : 4 and 4 : 5
So, both are not equivalent.

Question 14.
38 : 19 and 2 : 1
NO, pair of ratios are not equal.
Explanation:
38 : 19 and 2 : 1
2:1 and 1:2 [19 x 2 =38 and 19 x 1 = 19]
So, both are not equivalent.

Question 15.
12 : 8 and 18 : 12
YES, pair of ratios are equal.
Explanation:
12 : 8 and 18 : 12
3 : 2 and 3 : 2
So, both are equivalent.

Find the missing term in each pair of equivalent ratio.

Question 16.
7 : 9 = 49 :
Explanation:
product of extremes = product of means
a:b = c:d
$$\frac{a}{b}$$ = $$\frac{c}{d}$$
a = 7, b = 9, c = 49, d = x
7 x x = 9 x 49
7x = 441
x = $$\frac{441}{7}$$
x = 63

Question 17.
12 : 5 = 144 :
Explanation:
product of extremes = product of means
a:b = c:d
$$\frac{a}{b}$$ = $$\frac{c}{d}$$
a =12, b = 5, c = 144, d = x
12 x x = 5 x 144
12x = 720
x = $$\frac{720}{12}$$
x = 60

Question 18.
4 : 15 = 48 :
Explanation:
product of extremes = product of means
a:b = c:d
$$\frac{a}{b}$$ = $$\frac{c}{d}$$
a = 4, b = 15, c = 48, d = x
4 x x = 15 x 48
4x = 720
x = $$\frac{720}{4}$$
x = 180

Question 19.
7 : 13 = 77 :
Explanation:
product of extremes = product of means
a:b = c:d
$$\frac{a}{b}$$ = $$\frac{c}{d}$$
a = 7, b = 13, c = 77, d = x
7 x x = 13 x 77
7x = 1,001
x = $$\frac{1001}{7}$$
x = 143

Question 20.
45 : 36 = : 12
Explanation:
product of extremes = product of means
a:b = c:d
$$\frac{a}{b}$$ = $$\frac{c}{d}$$
a = 45, b = 36, c = x, d = 12
45 x 12 = 36 x x
36x = 540
x = $$\frac{540}{36}$$
x = 15

Question 21.
30 : 48 = : 8
Explanation:
product of extremes = product of means
a:b = c:d
$$\frac{a}{b}$$ = $$\frac{c}{d}$$
a = 30, b = 48, c = x, d = 8
30 x 8 = 48 x x
48x = 240
x = $$\frac{240}{48}$$
x = 5

Question 22.
72 : 84 = : 7
Explanation:
product of extremes = product of means
a:b = c:d
$$\frac{a}{b}$$ = $$\frac{c}{d}$$
a = 72, b = 84, c = x, d = 7
72 x 7 = 84 x x
504 = 84x
x = $$\frac{504}{84}$$
x = 6

Question 23.
121 : 88 = : 8
Explanation
product of extremes = product of means
a:b = c:d
$$\frac{a}{b}$$ = $$\frac{c}{d}$$
a = 121, b = 88, c = x, d = 8
121 x 8 = 88 x x
88x = 968
x = $$\frac{968}{88}$$
x = 11

Find the equivalent ratios.

Question 24.
Use multiplication to find three ratios equivalent to 8 : 12.
The three equivalent ratios of 8 : 12 are 16 : 24; 24: 36 and 32 : 48.
Explanation:
first we need to write the given ratio as fraction = 8/12
= (8 × 2)/(12 × 2)
= 16/24
= 16 : 24 (one equivalent ratio),
So, 16 : 24 is an equivalent ratio of 8 : 12.
Similarly again, we need to write the given ratio 8 : 12 as fraction to get another equivalent ratio = 8/12
= (8 × 3)/(12 × 3)
= 24/36 is another equivalent ratio.
Similarly again, we need to write the given ratio 8 : 12 as fraction to get another equivalent ratio = 8/12
= (8 × 4)/(12 × 4)
= 32/48 is another equivalent ratio.
Therefore, the three equivalent ratios of 8 : 12 are 16 : 24; 24: 36 and 32 : 48.

Question 25.
Use division to find all the whole number ratios equivalent to 168 : 56.
84 : 28; 56: 18 and 42 : 14.
Explanation:
first we need to write the given ratio as fraction = 168/56
= (168 ÷ 2)/(56 ÷ 2)
= 84/28
So, 168 : 56 is an equivalent ratio of 84 : 28.
Similarly again, we need to write the given ratio 168 : 56 as fraction to get another equivalent ratio = 168/56
= (168 ÷ 3)/(56 ÷ 3)
= 56/18
So, 168 : 56 is an equivalent ratio of 56 : 18.
Similarly again, we need to write the given ratio 168 : 56 as fraction to get another equivalent ratio = 168/56
= (168 ÷ 4)/(56 ÷ 4)
= 42/14
So, 168 : 56 is an equivalent ratio of 42 : 14.
Therefore, the two equivalent ratios of 168 : 56 are 84 : 28; 56: 18 and 42 : 14.

Copy and complete.

Question 26.
A manufacturer’s instruction states that 3 cups of cleaning agent should be diluted with 5 cups of water before use. Copy and complete the table.

Explanation:
A manufacturer’s instruction states that 3 cups of cleaning agent should be diluted with 5 cups of water before use.
ratio of cleaning agent and water = 3 : 5

Find the missing term of each pair of equivalent ratio.

Question 27.
63 : 27 = 49 :
Explanation:
the product of extremes = the product of means
a:b :: c:d  = > a x d = b x c
(27 x 49) /63 = 21
63 : 27 = 49 : 21

Question 28.
81 : 18 = 36 :
Explanation:
the product of extremes = the product of means
a:b :: c:d  = > a x d = b x c
(18 x 36) /81 = 648/81 = 8
81 : 18 = 36 : 8

Question 29.
24 : 96 = 5 :
Explanation:
the product of extremes = the product of means
a:b :: c:d  = > a x d = b x c
(96 x 5) /24 = 480/24 = 20
24 : 96 = 5 : 20

Question 30.
72 : 24 = 15 :
Explanation:
the product of means = the product of extremes
a:b :: c:d  = > a x d = b x c
(24 x 15) /72 = 360/72 = 5
72 : 24 = 15 : 5

Question 31.
60 : 144 = : 60
Explanation:
the product of means = the product of extremes
a:b :: c:d  = > a x d = b x c
(60 x 60) /144= 3600/144 = 25
60 : 144 = 25 : 60

Question 32.
125 : 80 = : 48
Explanation:
the product of extremes = the product of means
a:b :: c:d  = > a x d = b x c
(125 x 48) /80 = 6000/80 = 75
125 : 80 = 75 : 48

Question 33.
90 : 15 = : 7
Explanation:
the product of extremes = the product of means
a:b :: c:d  = > a x d = b x c
(90 x 7) /15 = 630/15 = 42
90 : 15 = 42 : 7

Question 34.
98 : 112 = 63 :
Explanation:
the product of extrems = the product of means
a:b :: c:d  = > a x d = b x c
(112 x 63) /98 = 7056/98 = 72
98 : 112 = 63 : 72

Solve.

Question 35.
Judy uses 5 ounces of lemonade concentrate for every 9 ounces of orange juice concentrate to make a fruit punch.

a) Find the ratio of the number of ounces of orange juice concentrate to the number of ounces of lemonade concentrate she uses.
9 : 5
Explanation:
Judy uses 5 ounces of lemonade concentrate for every 9 ounces of orange juice concentrate to make a fruit punch.
The ratio of the orange juice and lemonade = 9 : 5

b) If Judy uses 36 ounces of orange juice concentrate to make the fruit punch, how many ounces of lemonade concentrate does she use?
20 oz
Explanation:
If Judy uses 36 ounces of orange juice concentrate to make the fruit punch,
how many ounces of lemonade concentrate does she use
9 : 5 = 36 : ?
the product of means = the product of extremes
a:b :: c:d  = > a x d = b x c
(36 x 5) /9 = 180/9 = 20
9 : 5 = 36 : 20

c) If Judy uses 45 ounces of lemonade concentrate to make the fruit punch, how many ounces of orange juice concentrate does she use?
81 oz
Explanation:
If Judy uses 45 ounces of lemonade concentrate to make the fruit punch,
how many ounces of orange juice concentrate does she use
9 : 5 = ? : 45
the product of means = the product of extremes
a:b :: c:d  = > a x d = b x c
(9 x 45) /5 = 405/5 = 81
9 : 5 = 81 : 45

Question 36.
In a science experiment, Farah mixed a salt solution and vinegar in the ratio 3 : 7.
a) If she used 262.8 milliliters of salt solution1 how much vinegar did she use?
183.9ml
Explanation:
The ratio of vinegar to total mixture is 7 : 10
The 10 is 3 + 7.  Out of 10 ml, 3 will be Salt and 7 will be Vinegar.
7/10 = V/262.8
1839.6 = 10V
V = 183.9 ml

b) If 0.56 liter of vinegar was used, how much salt solution did she use?
78.84 ml
Explanation:
The ratio of salt to total mixture is 3 : 10
The 10 is 3 + 7.  Out of 10 ml, 3 will be Salt and 7 will be Vinegar.
3/10 = Salt/262.8
262.8 x 3 = 10S
788.4 = 10S
S = 788.4/10
S = 78.84 ml

Question 37.
A fruit seller packs different fruits into baskets of the same size. The ratio of the weight of bananas to the weight of apples to the weight of pears s the same for all the baskets. The table shows the different weights of fruits in the baskets. Copy and complete the table.

Explanation:
A fruit seller packs different fruits into baskets of the same size.
The ratio of the weight of bananas to the weight of apples to the weight of pears are the same for all the baskets.
The table shows the different weights of fruits in the baskets.
Find the largest common factor, of all the fruits.
46 apples = 8 x 6
30 pears = 5 x 6
24 bananas = 4 x 6
6 baskets each with 8 apples, 5 pears and 4 bananas.

## Math in Focus Grade 6 Chapter 3 Review Test Answer Key

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 3 Review Test to finish your assignments.

## Math in Focus Grade 6 Course 1 A Chapter 3 Review Test Answer Key

Concepts and Skills

Divide.

Question 1.
15 ÷ $$\frac{1}{3}$$

Explanation:
Dividing fractions is equal to the multiplication of a fraction by the reciprocal of another fraction. A fraction has a numerator and a denominator.
When we divide one fraction by another, we almost multiply the fractions.

$$\frac{15}{1}$$ ÷ $$\frac{1}{3}$$

$$\frac{15}{1}$$ x $$\frac{3}{1}$$

15 x 3 = 45

Question 2.
24 ÷ $$\frac{1}{6}$$

Explanation:
Dividing fractions is equal to the multiplication of a fraction by the reciprocal of another fraction. A fraction has a numerator and a denominator.
When we divide one fraction by another, we almost multiply the fractions.

24 ÷ $$\frac{1}{6}$$

24 x 6 = 144

Question 3.
$$\frac{3}{8}$$ ÷ $$\frac{3}{4}$$

$$\frac{1}{2}$$

Explanation:
Dividing fractions is equal to the multiplication of a fraction by the reciprocal of another fraction. A fraction has a numerator and a denominator.
When we divide one fraction by another, we almost multiply the fractions.

$$\frac{3}{8}$$ ÷ $$\frac{3}{4}$$

$$\frac{3}{8}$$ x $$\frac{4}{3}$$

$$\frac{12}{24}$$ = $$\frac{1}{2}$$

Question 4.
$$\frac{7}{12}$$ ÷ $$\frac{1}{3}$$

$$\frac{7}{3}$$

Explanation:
Dividing fractions is equal to the multiplication of a fraction by the reciprocal of another fraction. A fraction has a numerator and a denominator.
When we divide one fraction by another, we almost multiply the fractions.

$$\frac{7}{12}$$ ÷ $$\frac{1}{3}$$

$$\frac{7}{12}$$ x $$\frac{3}{1}$$

$$\frac{21}{12}$$ = $$\frac{7}{3}$$

Multiply.

Question 5.
0.3 × 8
Explanation:
Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,
then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.
0.3 x 8 = 2.4

Question 6.
6 × 0.7
Explanation:
Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,
then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.
6 x 0.7 = 4.2

Question 7.
0.28 × 6
Explanation:
Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,
then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.
0.28 x 6 = 1.68

Question 8.
7 × 0.068
Explanation:
Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,
then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.
7 x 0.068 = 0.476

Question 9.
0.3 × 0.6
Explanation:
Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,
then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.
0.3 x 0.6 = 0.18

Question 10.
0.5 × 0.8
Explanation:
Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,
then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.
0.5 x 0.8 = 0.4

Question 11.
5.7 × 0.4
Explanation:
Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,
then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.
5.7 x 0.4 = 2.28

Question 12.
9.3 × 0.89
Explanation:
Multiplication of decimals is done by ignoring the decimal point and multiply the numbers,
then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.
9.3 x 0.89 = 8.277

Divide.

Question 13.
6 ÷ 0.6
Explanation:
To divide a number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.
6 ÷ 0.6 = 10

Question 14.
8 ÷ 0.4
Explanation:
To divide a number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Question 15.
35 ÷ 0.7
Explanation:
To divide a number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Question 16.
88 ÷ 0.2
Explanation:
To divide a number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Question 17.
5 ÷ 0.25
Explanation:
To divide a number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Question 18.
8 ÷ 0.16
Explanation:
To divide a number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Question 19.
96 ÷ 0.16
Explanation:
To divide a number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Question 20.
396 ÷ 0.36
Explanation:
To divide a number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Question 21.
0.87 ÷ 0.03
Explanation:
To divide a decimal number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Question 22.
0.98 ÷ 0.7
Explanation:
To divide a decimal number by a decimal number,
multiply the divisor by as many tens as necessary until we get a whole number,
then remember to multiply the dividend by the same number of tens.

Problem Solving

Solve. Show your work.

Question 23.
In January, Jane volunteered at a hospital for a total of 12 hours. She spent $$\frac{4}{5}$$ hour at the hospital every time she volunteered. How many times did Jane volunteer in January?
15 times
Explanation:
In January, Jane volunteered at a hospital for a total of 12 hours.
She spent $$\frac{4}{5}$$ hour at the hospital every time she volunteered.
Number times Jane volunteer in January
$$\frac{12}{1}$$ ÷ $$\frac{4}{5}$$

$$\frac{12}{1}$$ x $$\frac{5}{4}$$
3 x 5 = 15

Question 24.
Paul is making loaves of raisin bread to sell at a fundraising event. The recipe calls for $$\frac{1}{3}$$ cup of raisins for each loaf, and Paul has 3$$\frac{1}{4}$$ cups of raisins.
a) How many loaves can Paul make?
Paul can make 9 loaves.
Explanation:
Paul has 3$$\frac{1}{4}$$ cups of raisins.

The recipe calls for $$\frac{1}{3}$$ cup of raisins for each loaf,

Number of loaves can Paul make are

$$\frac{13}{4}$$ ÷ $$\frac{1}{3}$$

$$\frac{13}{4}$$ x $$\frac{3}{1}$$

39 ÷ 4 = 9$$\frac{3}{4}$$

b) How many cups of raisins will he have left over?
$$\frac{3}{4}$$

Explanation:
Paul has 3$$\frac{1}{4}$$ cups of raisins.

The recipe calls for $$\frac{1}{3}$$ cup of raisins for each loaf,
Number of loaves can Paul make are

$$\frac{13}{4}$$ ÷ $$\frac{1}{3}$$

$$\frac{13}{4}$$ x $$\frac{3}{1}$$

39 ÷ 4 = 9$$\frac{3}{4}$$

Number of loaves left over are $$\frac{3}{4}$$

Question 25.
Jane has a dog that eats 0.8 pound of dog food each day. She buys a 40-pound bag of dog food. How many days will this bag of dog food last?
50 days
Explanation:
Jane has a dog that eats 0.8 pound of dog food each day.
She buys a 40-pound bag of dog food.
Number of days will this bag of dog food last

Question 26.
Mervin had some cartons of milk. He sold $$\frac{2}{5}$$ of the cartons of milk in the morning. He then sold $$\frac{3}{4}$$ of the remainder in the afternoon. 24 more cartons of milk were sold in the afternoon than in the morning. How many cartons of milk did Mervin have at first?
480 cartons of milk.
Explanation:
total 5 parts
each part can be sub divided in to 4 parts each
in each  box 24 cartons of milk
if total boxes are 20 and each box contains 24 cartons of milk
then the total number of milk is 24 x 20 = 480

Question 27.
Alice baked a certain number of pies. She gave $$\frac{1}{8}$$ of the pies to her friends and $$\frac{1}{4}$$ of the remainder to her neighbor. She was left with 63 pies. How many pies did Alice bake at first?
96 pies
Explanation:
Let the original count of pies be represented by x
She gave $$\frac{1}{8}$$ of the pies to her friend

So, x – $$\frac{1}{8}$$
A quarter of this given to the neighbor

x – $$\frac{x}{8}$$ – x – $$\frac{x}{8}$$ x $$\frac{1}{4}$$ = 63

$$\frac{8x – x}{8}$$ – $$\frac{8x – x}{8}$$ x $$\frac{1}{4}$$ = 63

$$\frac{7x}{8}$$ – $$\frac{7x}{8}$$ x $$\frac{1}{4}$$ = 63

$$\frac{7x}{8}$$ – $$\frac{7x}{32}$$ = 63

$$\frac{7x}{32}$$ – $$\frac{28x}{32}$$ = 63

Multiply both sides by $$\frac{32}{21}$$ x 63

x = 96

Question 28.
At a concert, $$\frac{2}{5}$$ of the people were men. There were 3 times as many women as children. If there were 45 more men than children, how many people were there at the concert?
180 people
Explanation:
Let people= p
men = $$\frac{2}{5}$$p
Let children = c
women = 3c
men = $$\frac{2}{5}$$p = c+45
people = men + women + children
= $$\frac{2}{5}$$p + 3c + c

= $$\frac{2}{5}$$p + 4c

= $$\frac{3}{5}$$p = 4c
$$\frac{2}{5}$$p = c + 45
Children = 27
people = 180
So, 180 people at the show.
women = 3c = 3 x 27 = 81
men = $$\frac{2}{5}$$p = c+45
= 72

Question 29.
$$\frac{3}{4}$$ of the students in a school were girls and the rest were boys. $$\frac{2}{3}$$ of the girls and $$\frac{1}{2}$$ of the boys attended the school carnival. Find the total number of students in the school if 330 students did not attend the carnival.
Total number of students 880
Explanation:
girls = 3boys,
since $$\frac{3}{4}$$ = 3 x $$\frac{1}{4}$$

$$\frac{2}{3}$$ girls + $$\frac{1}{2}$$ boys attended

$$\frac{2}{3}$$ x 3boys + $$\frac{1}{2}$$ boys

= $$\frac{5}{2}$$ boys attended

subtract that from the total (boys + girls) students:
boys + girls – $$\frac{5}{2}$$ boys = 330

4b – $$\frac{5}{2}$$ boys = 330

$$\frac{3}{2}$$ boys = 330
boys = 220
so, girls = 3b
= 220 x 3 = 660
Boys + Girls = (220 + 660) = 880
There are 880 students
660 girls and 220 boys
440 girls and 110 boys attended = 550
the remaining 330 did not attend.

Question 30.
At a baseball game, there were three times as many males as females. $$\frac{5}{6}$$ of the males were boys and the rest were men. $$\frac{2}{3}$$ of the females were girls and the rest were women. Given that there were 121 more boys than girls, how many adults were there at the baseball game?
Explanation:
Number of females x
Number of girls = $$\frac{2}{3}$$ x – girls

Number of women = $$\frac{1}{3}$$ x

Number of males = 3x

Number of boys = $$\frac{5}{6}$$ x 3x

= $$\frac{5}{2}$$ x – boys

Number of men = $$\frac{1}{6}$$ x 3x

= $$\frac{1}{2}$$ x – men
So, $$\frac{5}{2}$$ – 121 = $$\frac{2}{3}$$ x

$$\frac{15}{6}$$x – $$\frac{4}{6}$$x = 121

$$\frac{11}{6}$$x = 121
x = 66
Men = $$\frac{1}{2}$$ x 66 = 33

Women = $$\frac{1}{3}$$ x 66 = 22
Adults = Men + Women
Adults = 33 + 22 = 55
Question 31.
Mr. Thomas spent $1,600 of his savings on a television set and $$\frac{2}{5}$$ of the remainder on a refrigerator. He had $$\frac{1}{3}$$ of his original amount of savings left. a) What was Mr. Thomas’s original savings? Answer:$3600
b) What was the cost of the refrigerator?
$2400 Explanation: Let x is the savings, x(1600+(2x− $$\frac{1600}{5}$$) = x3 Because x is total amount of savings and he spent$1600
So, now he has 2÷5 of the total amount – \$1600
(x÷3 Because he has 1÷3 of his original amount of savings)
x+(16002x− $$\frac{3200}{5}$$) = x3
3x+3(1600+2x+ $$\frac{3200}{5}$$)=x
3x+(4800+6x+ $$\frac{9600}{5}$$)=x
3x+(48001.2x+1920)=x
2x=4800+1.2x1920.
8
x=2880
x=3600

Question 32.
Sue buys 8.5 pounds of chicken to make tacos. She uses 0.3 pound of chicken for each taco.
a) How many tacos can Sue make?
Sue can make 28 tacos
b) How many pounds of chicken are left over?
$$\frac{1}{3}$$ left over
Explanation:
Sue buys 8.5 pounds of chicken to make tacos.
She uses 0.3 pound of chicken for each taco.
$$\frac{8.5}{0.3}$$
= 28 $$\frac{1}{3}$$

## Math in Focus Grade 6 Chapter 3 Lesson 3.2 Answer Key Multiplying Decimals

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 3 Lesson 3.2 Multiplying Decimals to finish your assignments.

## Math in Focus Grade 6 Course 1 A Chapter 3 Lesson 3.2 Answer Key Multiplying Decimals

### Math in Focus Grade 6 Chapter 3 Lesson 3.2 Guided Practice Answer Key

Complete.

Question 1.
Multiply 0.9 by 4.

The multiplication of  0.9 by 4 is 3.6.

Explanation:
The multiplication of  0.9 by 4 is 3.6.

Question 2.
Multiply 0.025 by 3.

Explanation:
The multiplication of 0.025 by 3 is 0.075.

Multiply.

Question 3.

The multiplication of 0.07 × 9 is 0.63.

Explanation:
The multiplication of 0.07 × 9 is 0.63.

Question 4.

The multiplication of 0.14 × 3 is 0.42.

Explanation:
The multiplication of 0.14 × 3 is 0.42.

Question 5.

The multiplication of 0.045 × 7 is 0.315.

Explanation:
The multiplication of 0.045 × 7 is 0.315.

Write in vertical form. Then multiply and decide where to place the decimal point.

Question 6.
0.32 × 8
0.32 × 8 = 2.56.

Explanation:
The multiplication of 0.32 × 8 is 2.56.

Question 7.
9 × 0.24
9 × 0.24 = 2.16.

Explanation:
The multiplication of 9 × 0.24 is 2.16.

Question 8.
0.057 × 6
0.057 × 6 = 0.342.

Explanation:
The multiplication of 0.057 × 6 is 0.342.

Complete.

Question 9.
Find 0.3 × 0.6.

The multiplication of 0.3 × 0.6 is 0.18.

Explanation:
The multiplication of 0.3 × 0.6 is
0.3 × 0.6 = $$\frac{3}{10}$$ × $$\frac{6}{10}$$
= $$\frac{18}{100}$$
= 0.18.

Question 10.
Find 0.9 × 0.8.

The multiplication of 0.9 × 0.8 is 0.72.

Explanation:
The multiplication of 0.9 × 0.8 is

Complete.

Question 11.
Find 3.2 × 0.6

The multiplication of 3.2 × 0.6 is 1.92.

Explanation:
The multiplication of 3.2 × 0.6 is

Write in vertical form. Then multiply and decide where to place the decimal point.

Question 12.
4.3 × 5.7
The multiplication of 4.3 × 5.7 is 24.51.

Explanation:
The multiplication of 4.3 × 5.7 is

Complete.

Question 13.
Find 0.89 × 0.4

The multiplication of 0.89 × 0.4 is 0.356.

Explanation:
The multiplication of 0.89 × 0.4 is

Write in vertical form. Then multiply and decide where to place the decimal point.

Question 14.
4.3 × 5.7
The multiplication of 4.3 × 5.7 is 24.51.

Explanation:
The multiplication of 4.3 × 5.7 is

Hands-On Activity

Materials

• graph paper
• ruler

Finding the factors of a decimal.

Step 1.
Draw four 10 × 10 squares on graph paper.

Step 2.
Mark each side from 0 to 1 as shown.

Step 3.
a) Find two decimals that give a product of 0.12.
× = 0.12
Show and shade 0.12 on the grids in two different ways.
Example
0.2 × 0.6 = 0.12

b) Find two decimals that give a product of 0.36. Show and shade 0.36 on the grids in two different ways.
0.6 × 0.6 = 0.36.

Explanation:
The two decimals that give a product of 0.36 is 0.6 × 0.6.

### Math in Focus Course 1A Practice 3.2 Answer Key

Complete.

Question 1.
0.3 × 4 is the same as groups of .
0.3 groups of 4.

Explanation:
Here 0.3 × 4 is the same as 0.3 groups of 4.

Question 2.
7 × 0.8 is the same as groups of .
7 groups of 0.8.

Explanation:
Here 7 × 0.8 is the same as 7 groups of 0.8.

Write a multiplication statement that represents each number line.

Question 3.

3×0.5 = 1.5.

Explanation:
The multiplication statement that represents the number line is 3×0.5 = 1.5.

Question 4.

6×0.9 = 5.4.

Explanation:
The multiplication statement that represents the number line is 6×0.9 = 5.4.

Write in vertical form. Then multiply.

Question 5.
0.9 × 12
The multiplication of 0.9 × 12 is 10.8.

Explanation:
The multiplication of 0.9 × 12 is
9                          0.9
×  12                       × 12
_____               ———
108                     10.8

Question 6.
0.47 × 5
The multiplication of 0.47 × 5 is 2.35.

Explanation:
The multiplication of 0.47 × 5 is
47 × 5 = 235
0.47 × 5 = 2.35

Question 7.
0.063 × 9
0.063 × 9 = 0.67.

Explanation:
The multiplication of 0.063 × 9 is
63 × 9 = 567
0.063 × 9 = 0.567.

Question 8.
00.85 × 11
The multiplication of 00.85 × 11 is  9.35.

Explanation:
The multiplication of 00.85 × 11 is
85 × 11 = 935,
00.85 × 11 = 9.35.

Question 9.
00.1 × 0.2
The multiplication of 00.1 × 0.2 is 0.02.

Explanation:
The multiplication of 00.1 × 0.2 is
1 × 2 = 2,
00.1 × 0.2 = 0.02.

Question 10.
0.2 × 0.3
The multiplication of 0.2 × 0.3 is

Explanation:
The multiplication of 0.2 × 0.3 is
2 × 3 = 6
0.2 × 0.3 = 0.06.

Question 11.
0.4 × 0.4
The multiplication of 0.4 × 0.4 is 0.16.

Explanation:
The multiplication of 0.4 × 0.4 is
4 × 4 = 16,
0.4 × 0.4 = 0.16.

Question 12.
0.6 × 0.7
The multiplication of 0.6 × 0.7 is 0.42.

Explanation:
The multiplication of 0.6 × 0.7 is
6 × 7 = 42,
0.6 × 0.7 = 0.42.

Question 13.
0.7 × 0.9
The multiplication of 0.7 × 0.9 is 0.63.

Explanation:
The multiplication of 0.7 × 0.9 is
7 × 9 = 63,
0.7 × 0.9 = 0.63.

Multiply mentally.

Question 14.
0.7 × 8
The mental multiplication of 0.7 × 8 is 5.6.

Explanation:
The mental multiplication of 0.7 × 8 is
0.7 × 8 = $$\frac{7}{10}$$ × 8
= $$\frac{7}{5}$$ × 4
= $$\frac{28}{5}$$
= 5.6.

Question 15.
0.9 × 9
The mental multiplication of 0.9 × 9 is 8.1.

Explanation:
The mental multiplication of 0.9 × 9 is
0.9 × 9 = $$\frac{9}{10}$$ × 9
= $$\frac{81}{10}$$
= 8.1.

Question 16.
0.9 × 11
The mental multiplication of 0.9 × 11 is 9.9.

Explanation:
The mental multiplication of 0.9 × 11 is
0.9 × 11 = $$\frac{9}{10}$$ × 11
= $$\frac{99}{10}$$
= 9.9.

Question 17.
0.7 × 0.4
The mental multiplication of 0.7 × 0.4 is $$\frac{14}{50}$$.

Explanation:
The mental multiplication of 0.7 × 0.4 is
0.7 × 0.4 = $$\frac{7}{10}$$ × $$\frac{4}{10}$$
= $$\frac{7}{10}$$ × $$\frac{2}{5}$$
= $$\frac{14}{50}$$.

Question 18.
0.8 × 0.6
The mental multiplication of 0.8 × 0.6 is 0.48.

Explanation:
The mental multiplication of 0.8 × 0.6 is
0.8 × 0.6 = $$\frac{8}{100}$$ × $$\frac{6}{100}$$
= $$\frac{48}{100}$$
= 0.48.

Question 19.
0.3 × 0.9
The mental multiplication of 0.3 × 0.9 is 0.27.

Explanation:
The mental multiplication of 0.3 × 0.9 is
0.3 × 0.9 = $$\frac{3}{100}$$ × $$\frac{9}{100}$$
= $$\frac{27}{100}$$
= 0.27.

Question 20.
0.7 × 0.7
The mental multiplication of 0.7 × 0.7 is 0.49.

Explanation:
The mental multiplication of 0.7 × 0.7 is
0.7 × 0.7 = $$\frac{7}{100}$$ × $$\frac{7}{100}$$
= $$\frac{49}{100}$$
= 0.49.

Question 21.
0.5 × 0.9
The mental multiplication of 0.5 × 0.9 is 0.45.

Explanation:
The mental multiplication of 0.5 × 0.9 is
0.5 × 0.9 = $$\frac{5}{10}$$ × $$\frac{9}{10}$$
= $$\frac{45}{100}$$
= 0.45.

Question 22.
0.8 × 0.9
The mental multiplication of 0.8 × 0.9 is 0.72.

Explanation:
The mental multiplication of 0.5 × 0.9 is
0.8 × 0.9 = $$\frac{8}{10}$$ × $$\frac{9}{10}$$
= $$\frac{72}{100}$$
= 0.72.

Question 23.
0.15 × 6
The mental multiplication of 0.15 × 6 is 0.9.

Explanation:
The mental multiplication of 0.15 × 6 is
0.15 × 6 = $$\frac{15}{100}$$ × $$\frac{6}{10}$$
= $$\frac{90}{100}$$
= 0.9

Question 24.
0.22 × 4
The mental multiplication of 0.22 × 4 is 0.88.

Explanation:
The mental multiplication of 0.22 × 4 is
0.22 × 4 = $$\frac{22}{100}$$ ×4
= $$\frac{88}{100}$$
= 0.88.

Question 25.
0.25 × 3
The mental multiplication of 0.25 × 3 is 0.75.

Explanation:
The mental multiplication of 0.25 × 3 is
0.25 × 3 = $$\frac{25}{100}$$ × 3
= $$\frac{75}{100}$$
= 0.75.

Question 26.
0.032 × 5
The mental multiplication of 0.032 × 5 is 0.16.

Explanation:
The mental multiplication of 0.032 × 5 is
0.032 × 5 = $$\frac{32}{1000}$$ × 5
= $$\frac{160}{1000}$$
= 0.16.

Question 27.
0.04 1 × 8
The mental multiplication of 0.04 1 × 8 is 0.328.

Explanation:
The mental multiplication of 0.04 1 × 8 is
0.04 1 × 8 = $$\frac{41}{1000}$$ × 8
= $$\frac{41}{1000}$$ × 8
= $$\frac{328}{1000}$$
= 0.328.

Question 28.
0.055 × 9
The mental multiplication of 0.055 × 9 is 0.495.

Explanation:
The mental multiplication of 0.055 × 9 is
0.055 × 9 = $$\frac{55}{1000}$$ × 9
= $$\frac{495}{1000}$$
= 0.495.

Write in vertical form. Then multiply.

Question 29.
1.2 × 0.6
The multiplication of 1.2 × 0.6 is 0.72.

Explanation:
The multiplication of 1.2 × 0.6 is
12 × 06 = 72,
1.2 × 0.6 = 0.72.

Question 30.
0.89 × 1.2
The multiplication of 0.89 × 1.2 is 1.068.

Explanation:
The multiplication of 0.89 × 1.2 is
89 × 12 = 1,068,
0.89 × 1.2 = 1.068.

Question 31.
2.3 × 1.5
The multiplication of 2.3 × 1.5 is 3.45.

Explanation:
The multiplication of 2.3 × 1.5 is
23 × 15 = 345,
2.3 × 1.5 = 3.45.

Question 32.
3.4 × 6.7
The multiplication of 3.4 × 6.7 is 22.78.

Explanation:
The multiplication of 3.4 × 6.7 is
34 × 67 = 2,278.
3.4 × 6.7 = 22.78.

Question 33.
4.9 × 6.3
The multiplication of 4.9 × 6.3 is 30.87.

Explanation:
The multiplication of 4.9 × 6.3 is
49 × 63 = 3,087,
4.9 × 6.3 = 30.87.

Question 34.
5.8 × 7.8
The multiplication of 5.8 × 7.8 is 45.24.

Explanation:
The multiplication of 5.8 × 7.8 is
58 × 78 = 4,524,
5.8 × 7.8 = 45.24.

Question 35.
0.46 × 1.3
The multiplication of 0.46 × 1.3 is 0.598.

Explanation:
The multiplication of 0.46 × 1.3 is
46 × 13 = 598.
0.46 × 1.3 = 0.598.

Question 36.
0.705 × 0.5
The multiplication of 0.705 × 0.5 is 0.3525.

Explanation:
The multiplication of 0.705 × 0.5 is
705 × 5 = 3,525,
0.705 × 0.5 = 0.3525.

Question 37.
0.597 × 0.21
Math Journal Your friend knows how to find the product $$\frac{57}{100}$$ × $$\frac{3}{10}$$. However, your friend does not know how to find the product 0.57 × 0.3. Write an explanation that will help your friend understand how to multiply the two decimals.
Here the product of $$\frac{57}{100}$$ × $$\frac{3}{10}$$ is $$\frac{171}{100}$$ which is 1.71 and to find the product of 0.57 × 0.3 first we will multiply 57 × 3 which is 171 and then we will place decimal, so the product will be 1.71.