Multiplication of Fractions Day 1 Warm-up · Multiplication of Fractions Day 1 Warm-up 1. List all...

Multiplication of Fractions Day 1 Warm-up

1. List all the symbols and words you can think of that mean “multiply”.

Symbols: Words:

2. Does multiplication make numbers bigger or smaller?

3. If you have two groups of six pizzas, how many pizzas do you have?

3. What operation (+, -, •, or ÷) did you use to get your answer to #3?

4. If you have 𝟏

𝟐of a group of 6 pizzas, how many pizzas do you have?

5. What operation do you think you used to get the answer to #5?

Name:_______________ Date: ____________ Class: ___________

Mult/Div 1

As you discussed the warmup, you proved conclusively that:

6 • 𝟏

𝟐= 3

But we don’t want to discuss pizzas every time we multiply. So we ask ourselves this question:

Question: How do you multiply a whole number by a fraction, … like 6 • 𝟏

𝟐?

Answer: Follow five simple steps, starting with the First-Two-Step Rap.

Multiplication (and division) First-Two-Step Rap:

When you __________ and when you __________ ,Line those numbers up from _______ ____ _______ .Ask yourself, what’s my first action?Change _______ and ________ numbers to ________ ________ !

Multiplying Whole Numbers and Fractions using Five Simple Steps

1. Make sure the numbers are lined up from side to side!

________ 6 _________ 6 • 𝟏

𝟐

• 𝟏

𝟐

2. Change whole numbers to improper fractions. •

3. Simplify before multiplying. • =

5. Put in simplest form!

Multiplying Fractions and Whole Numbers – More Practice!More Whole Numbers • Fractions: Fractions • Fractions (skip step 2!)

a. 6 •𝟏

𝟒= b. (6)(𝟐

𝟑) = c. (𝟏

𝟐)(𝟑

𝟒) = d.

𝟑

𝟓•

𝟓

𝟗=

Name:________________________ Date: ____________ Class: ___________

Multiplication of Fractions Notes

4. Multiply numerators. Multiply denominators.

Mult/Div 2

Name:________________________ Date: ____________ Class: ___________

Fraction Multiplication Worksheet (Proper Fractions / Whole Numbers)

Remember the steps for multiplication:1. Line numbers up from side to side2. Change whole numbers to fractions3. Simplify first if possible4. Multiply numerators and denominators5. Put answer in simplest form

1. Evaluate. Write all answers in simplest form!

a. (3

4)(5

7) b.

2

3x

2

3c.

1

4•

3

8d.

4

5(6

7)

e. 2

5•

1

2f. (3

4)(4

7) g.

6

7(4

9) h.

5

12x 8

i. 3

8•

2

3j.

4

5•

15

28k. (6)(3

4) l.

9

20p when p =

5

21

m. 7

8x

7

10n.

14

15•

10

18o. (42

51) (17

49) p. y • 10 when y =

14

25

(3)(4

5)

2

9•

3

4

1 1

3 2

2

9•

3

4

(3

1)(4

5)

12

5

22

5

1

6

Mult/Div 3

Name:________________________ Date: ____________ Class: ___________

2. Word Problems! Use multiplication of fractions to solve problems a - d below:

a. Jimmy eats 7

8cookies per minute for 6 minutes. How many cookies does he eat?

b. Deepah has a recipe that calls for 2

3cups of sugar. She wants to make

1

4of the

recipe. How many cups of sugar does she need?

c. Tomiko looks in her refrigerator and sees that she has 4

5of a gallon of milk. She

pulls it out and drinks 3

4of the

4

5of a gallon. How much milk does she drink?

d. The fence in Hans’ backyard is now 9

10built. Hans did

5

6of the work. What

fraction of the whole fence has Hans built?

3. Describe at least one way that multiplying fractions is similar to multiplying whole numbers.

4. Describe at least one way that multiplying fractions is different than multiplying whole numbers.

Fraction Multiplication (Proper Fractions / Whole Numbers - Cntd)

Mult/Div 4

Multiplication of Fractions Day 2 Warm-up

1. Find the products: 2

3• 9 = 6 •

3

4=

2. Use your answers above and any observations to you have made over the past few days to fill in the blanks below:

a. When you multiply any number by a number greater than one, the product is always ________ ________ (“less than” / “greater than”) the number you started with.

b. When you multiply any number by a number less than one, the product is always ________ ________ (“less than” / “greater than”) the number you started with.

3. Noah multiplied 3𝟓

𝟔•

𝟑

𝟒and obtained a product of 4

𝟕

𝟖. Without

multiplying these two numbers, explain why this answer is NOT REASONABLE!

4. Sadie evaluated the word problem below and determined that the

answer was 1𝟐

𝟑cookies. Without evaluating (without multiplying, dividing,

adding, or subtracting the numbers in the problem), explain why her answer is NOT REASONABLE.

Sadie’s problem: If Mary Ellen can eat 1𝟕

𝟖cookies each minute, how

many can she eat in 2𝟐

𝟓minutes?

Name:_______________ Date: ____________ Class: ___________

Mult/Div 5

Question: How do you multiply two mixed numbers … like 3𝟏

𝟓• 4

𝟏

𝟔?

Answer: Follow five simple steps, starting with the First-Two-Step Rap.


When you __________ and when you __________ …Line those numbers up from _______ ____ _______ .Ask yourself, what’s my first action?Change _______ and ________ numbers to ________ ________ !

Multiplying Mixed Numbers using Five Simple Steps

1. Make sure the mixed numbers are lined up from side to side!

________ 3𝟏

𝟓_________ 3

𝟏

𝟓• 4

𝟏

𝟔

• 4𝟏

𝟔

2. Change mixed numbers to improper fractions •

3. Simplify before multiplying • =


Multiplying Mixed Numbers – More Practice!

1. 2𝟏

𝟒• 3

𝟏

𝟑= 2. (6)(4

𝟏

𝟖) = 3. 2

𝟐

𝟕•

𝟑

𝟒= 4.

𝟑

𝟓• 3

𝟏

𝟑=

Name:________________________ Date: ____________ Class: ___________

Mixed Number Multiplication Notes / Poetry


Mult/Div 6

Name:________________________ Date: ____________ Class: ___________

Multiplication of Mixed Numbers Worksheet

Remember the steps for multiplication:

1. Change mixed and whole numbers to fractions

2. Simplify (cancel) before multiplying

3. Multiply numerators and denominators

4. Put in simplest form


a. (5)(3

4) b. 7 x

2

3c.

1

4• 11 d.

2

3(6)

e. 8 • 5

6f. (3

4)(6) g.

7

10(12) h. 10 x

3

5

i. 31

2• 3 j. 1

3

4• 6 k. (10)(1

4

15) l. 4p when p = 2

2

3

(6) (3

4) 4

1

2• 2

2

3

(6

1) (3

4)

9

2•

8

3

(6

1) (3

4)

9

2•

8

3

3

2

3 4

11

9

2

12

1

4𝟏

𝟐12

7

1•

2

3=

14

3

= 42

3

Mult/Div 7

Name:________________________ Date: ____________ Class: ___________

3. Use multiplication of mixed numbers to solve problems a - c:

a. Horatio eats 22

3cookies per minute for 8

1

4minutes. How many cookies does he eat?

b. Estevan has written 33

4pages on his research paper. Jessica has written 6 times as

many pages as Estevan. How many pages has Jessica written?

c. Sugi has eaten 21

2pieces of chicken. Each piece of chicken has 2

2

5grams of fat.

How many grams of fat has Sugi eaten?

4. Zephaniah multiplies 5𝟏

𝟐• 3

𝟐

𝟑and gets 11

𝟏

𝟔as his answer. Without multiplying

these two numbers, explain why this answer is unreasonable.

Multiplication of Mixed Numbers Worksheet (Continued)


a. 31

2• 2

1

3b. 1

2

5• 4

1

2c. (1

1

3)(2

1

2) d. 3

1

3y when y = 2

1

4

e. 31

5x 1

1

4f. 1

3

10• 2

1

2g. (5

1

4) (4

2

3) h. ab when a = 2

1

7, b = 4

1

5

Mult/Div 8

Division of Fractions Day 1 Warm-up

1. List all the symbols and words you can think of that mean “multiply”.

Symbols: Words:

2. Does division make numbers bigger or smaller?

3. If you have six pizzas and split them into groups of two, how many groups of two pizzas do you have?

4. What operation (+, -, •, or ÷) did you use to get your answer to #3?

5. If you have 6 pizzas and split them into groups of 𝟏

𝟐, how many

pizzas do you have?

6. What operation do you think you used to get the answer to #5?

7. Is there a similar multiplication problem involving 6 and 2 that would give you the same answer as the answer you got for #5?

Name:_______________ Date: ____________ Class: ___________

Mult/Div 9

After doing the warmup, you proved conclusively that:

6 ÷𝟏

𝟐= 12

You also discovered that this has a similar multiplication problem:

6 • 2 = 12

But we still haven’t figured out exactly how division works mathematically, so we ask this question:

Question: How do you divide a whole number by a fraction, … like 6 ÷𝟏

𝟐?

Answer: Follow five simple steps, using the First-Two-Step Rap and Copy-Dot-Flip Rap.


When you __________ and when you __________ ,Line those numbers up from _______ ____ _______ .Ask yourself, what’s my first action?Change _______ and ________ numbers to ________ ________ !

Copy-Dot-Flip Rap:

When you do _________ , I’ll give you a tip!Don’t forget to ______ , ______ , ______ !

Dividing Whole Numbers and Fractions using Five Simple Steps

1. Line the numbers up from side to side! _____ 6 ________ 6 ÷𝟏

𝟐

÷𝟏

𝟐

2. Change whole numbers to improper fractions. ÷3. COPY, DOT, FLIP.

•

4. Simplify and multiply • =


Name:________________________ Date: ____________ Class: ___________

Division of Fractions Notes (Fractions and Whole Numbers)

Copy Dot Flip

Mult/Div 10

Name:________________________ Date: ____________ Class: ___________

Remember the steps for division:1. Line numbers up from side to side2. Change whole numbers to fractions

3. Copy, dot, flip4. Simplify and multiply5. Put answer in simplest form


a. 5 ÷3

4b.

2

3÷ 7 c. 9 ÷

3

8d.

4

5

10

e. 2

5÷

1

2f.

3

4÷

7

8g.

5

6÷

4

9h.

5

12

7

8

i. 3

8÷

3

4j.

3

4÷

3

8k. 6 l.

9

20÷ p when p =

3

103

4

m. 7

8÷

7

10n.

6

7÷

6

7o.

42

51÷

14

17p.

𝑦

10when y =

5

6

6 ÷ 2

3

8

9•

15

4=

10

3

8

9÷

4

156

1÷ (2

3)

93

1

3

6

1• (3

2) = 9

1

3

1

flip

2 5

13

Remember: Top dog goes first!

= 𝟒

𝟓÷

𝟏𝟎

𝟏

Fraction Division Worksheet (Proper Fractions / Whole Numbers)

Mult/Div 11

Name:________________________ Date: ____________ Class: ___________

2. Word Problems! Use division of fractions to solve problems a -d below:

a. Georgianne eats 7

8cookies per minute. How long will it take her to eat 6 cookies?

b. Satvinder has a cake recipe that calls for 3

4cups of sugar. He has

1

2cups of

sugar. How many cakes can he make?

c. Kyoshi looks in his refrigerator and sees that he has 4

5of a gallon of milk. Each

glass that he drinks contains 1

10of a gallon. How many glasses can he drink with

the 4

5of a gallon?

d. A pencil is 3

8of an inch wide. A pencil box is 2 inches wide. How many pencils can

fit into the pencil box side by side?

3. Describe at least one way that multiplying fractions is similar to dividing fractions.

4. Describe at least one way that multiplying fractions is different than dividing fractions.

Fraction Division (Proper Fractions / Whole Numbers - Cntd)

Mult/Div 12

Division of Fractions Day 2 Warm-up

1. Find the quotients: 3

4÷ 9 = 6 ÷

3

4=

2. Use your answers above and any observations to you have made over the past few days to fill in the blanks below:

a. When you divide a larger number by a smaller number the quotient is always ________ ________ (“less than” / “greater than”) one.

b. When you divide a smaller number by a larger number the quotient is always ________ ________ (“less than” / “greater than”) one.

3. Sven divided 1𝟏

𝟑÷ 3

𝟓

𝟔and obtained a quotient of 2

𝟕

𝟖. Without

dividing these two numbers, explain why this answer is NOT REASONABLE!

4. Latifa evaluated the word problem below and determined that the

answer was 𝟏𝟒

𝟏𝟕minutes. Without evaluating (without multiplying,

dividing, adding, or subtracting the numbers in the problem), explain why her answer is NOT REASONABLE.

Latifa’s problem: If Sully can eat 1𝟑

𝟒cookies each minute, how long

will it take him to eat 2𝟏

𝟖cookies?

Name:_______________ Date: ____________ Class: ___________

Mult/Div 13

Question: How do you divide two mixed numbers … like 3𝟏

𝟓÷ 2

𝟐

𝟑?

Answer: Follow six simple steps, using the First-Two-Step Rap and Copy-Dot-Flip Rap!

Multiplication and Division First-Two-Step Rap:

When you ______________ and when you ______________ …Line those numbers up from _________ _____ _________ .Ask yourself, what’s my first action?Change ________ and _________ numbers to __________ __________ !

Copy-Dot-Flip Rap:

When you do __________ , I’ll give you a tip!Don’t forget to ________ , ________ , ________ !

Dividing Mixed Numbers using Six Simple Steps

1. Make sure the mixed numbers are lined up from side to side!

________ 3𝟏

𝟓_________ 3

𝟏

𝟓÷ 2

𝟐

𝟑

÷ 2𝟐

𝟑

2. Change to improper fractions ÷3. COPY, DOT, FLIP

4. Simplify before multiplying • =


Dividing Mixed Numbers – More Practice!

1. 2𝟏

𝟒÷ 3

𝟏

𝟐= 2. 10 ÷ 6

𝟏

𝟒= 3. 2

𝟐

𝟕4.

𝟓

𝟔÷ 3

𝟏

𝟑=

1𝟏

𝟑

Name:________________________ Date: ____________ Class: ___________

Mixed Number Division Notes / Poetry


Copy Dot Flip

Mult/Div 14

Name:________________________ Date: ____________ Class: ___________

1. Line numbers up from side to side2. Change mixed/whole numbers to fractions

3. Copy, dot, flip4. Simplify and multiply5. Put answer in simplest form


a. 21

3÷

3

4b. 1

1

6÷ 7 c. 8 ÷ 1

1

9d. 2

4

5

4

e. 5

6÷ 2

1

2f. 2

2

3÷ 1

1

6g. 2

1

7÷ 1

1

2h. 5

1

3

31

5

i. 13

8÷ 10 j. 5 ÷ 2

1

4k.

3

4l. 2

1

10÷ p when p = 1

2

5

6

m. 21

3÷ 1

1

6n. 1

1

6÷ 2

1

3o. 5

1

10÷ 2

1

8p.

𝑦1

6

when y = 12

3

41

6÷ 5

8

10

3•

1

2=

5

3

31

3÷ 2

25

6÷ 5

8

62

3 12

3

25

6• 8

5= 20

3

5

1

do

t

flip

5

1

10

3÷

2

1

3

4

Fraction Division Worksheet (Mixed Numbers)

Mult/Div 15

Name:________________________ Date: ____________ Class: ___________

2. Word Problems! Use division of fractions to solve problems a -d below. Make sure your answers are REASONABLE!

a. Peggy eats 17

8cookies per minute. How long will it take her to eat 2

1

2cookies?

b. Biff and Brandi’s recipe calls for 11

4cups of cocoa powder per batch. They have

31

8cups of cocoa powder. How many batches can they make?

c. At a national hot dog eating competition, Rolf eats 22

3hot dogs each minute.

How long will it take him to eat 15

6hot dogs?

d. Each book is 1

2of an inch wide. The book shelf is 25

1

2inches wide. How many

books can fit on the shelf?

3. Jomo divides 1𝟕

𝟒𝟑÷ 4

𝟏𝟕

𝟐𝟐and gets an answer more than 2. Without dividing,

explain why this answer is unreasonable.

4. Explain the error that Jahekah makes in evaluating this expression.

2

3𝟐

𝟑

= 32

3÷ 2 =

11

3÷

2

1=

11

3•

1

2=

11

6= 1

5

6

Fraction Division Worksheet (Mixed Numbers - Continued)

Mult/Div 16

Multiplication/Division Review Warm-up

1. 33

4÷ 6 = 4

1

5÷ 2

1

10= 1

3

4• 6 = 7

1

2• 1

1

5=

2. For each problem below, state whether you would MULTIPLY or DIVIDE to get your answer (do not solve the problems):

a. Baby Zoey crawls 2 feet each second. How many seconds will it take her to crawl 10 feet?

b. Baby Zoey crawls 2 feet each second. How many feet can she crawl in 10 seconds?

c. Baby Chloe crawls 3𝟏

𝟒feet each second. How many feet can she crawl in 5

𝟏

𝟑

seconds?

d. Baby Chloe crawls 3𝟏

𝟒feet each second. How many seconds will it take her to

crawl 5𝟏

𝟑feet?

3. For each problem below, state whether the answer you would expect to get would be LESS THAN ONE or MORE THAN ONE (do not solve the problems):

a. James can eat 2𝟏

𝟑cookies each minute. How many minutes will it take him to

eat 1𝟓

𝟔cookies?

b. You have 2𝟏

𝟏𝟔cups of cocoa powder. Each batch of brownies requires 1

𝟏

𝟒cups.

How many batches can you make?

c. Each candy bar contains 1𝟏

𝟑grams of fat. How many grams of fat are in 1

𝟑

𝟓

candy bars?

d. There are 2𝟐

𝟑doughnuts in the refrigerator. If three friends want to split

them up equally, how many doughnuts will each friend get?

Name:_______________ Date: ____________ Class: ___________

Mult/Div 17

Mult/Div 18

Name:________________________ Date: ____________ Class: ___________

Multiplication and Division of Fractions REVIEW SHEET

1. Evaluate. Write all answers in simplest form! SHOW ALL WORK!

a. 1

3•

5

8b.

3

8÷

2

9c.

3

4÷

7

10d. (4

5)(15

16)

e. 3

5(10) f.

2

3÷ 6 g. 2 x

5

8h. 12

3

7

i. 11

6÷ 4 j. 2

1

6• 4 k. 6 l. 5p when p = 1

2

15

22

3

m. 31

2÷ 1

2

5n. (1

2

5)(2

1

3) o. 2

1

10• 2

1

2p.

𝑦

41

6

when y = 12

3

q. 12

5• 2

1

2÷

1

4r. 3

1

2÷

3

4• 1

2

7

Mult/Div 19

Name:________________________ Date: ____________ Class: ___________

2. Word Problems! Use multiplication or division of fractions to solve problems a - d below. Make sure your answers are REASONABLE!

a. Sugi can walk 22

5miles each hour. How many miles can he walk in 2

1

4hours?

b. Sugi can walk 31

3miles each hour. How long will it take him to walk 2

1

2miles?

c. Ginny is drinking milk that contains 2

3grams of fat per cup. How many cups of milk

will she need to drink to reach 7 grams of fat?

d. Ginny is drinking milk that contains 2

3grams of fat per cup. How many grams of fat

will she drink if she drinks 7 cups of milk?

3. Long divides 5𝟕

𝟏𝟔÷ 1

𝟕

𝟐𝟓and gets an answer less than 1. Without dividing these

two numbers, explain why this answer is unreasonable.

4. Lionel multiplies 3𝟏

𝟒•

𝟓

𝟔and obtains 4

𝟏

𝟐𝟒as her answer. Without multiplying

these two numbers, explain why this answer is unreasonable.

Multiplication and Division of Fractions REVIEW SHEET (continued)

Mult/Div 20

Multiplication of Fractions Day 1 Warm-up · Multiplication of Fractions Day 1 Warm-up 1. List all...

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