Multiplying Mixed Numbers

English

Spanish

2.4 Multiplying Mixed Numbers

STATE STANDARDS

MA.6.A.1.1 MA.6.A.1.2 MA.6.A.1.3 MA.6.A.5.3

by a fraction?

How do you multiply a mixed number

1 ACTIVITY: Multiplying a Mixed Number and a Fraction

Work with a partner. Use a diagram to find the product.

a.

Sample:

1--1

?

2 --

2 3

What is two-thirds of 1--1?

2

Think

of

1

1 2

as

three

halves.

1

1

1

2

2

2

Two of the halves is 1.

1

1

1

2

2

2

So,

1--1

?

2 --

=

1.

2 3

b. --4 ? 2--1

9 4

c.

2

1 --

?

1 --

4 2

d.

-- 1

?

3

3 --

3 4

2 ACTIVITY: Multiplying a Mixed Number and a Fraction

Work with a partner. How many square feet are in the piece of fabric?

1

1 4

ft

1 2

ft

a. Use the Distributive Property and find the sum of the two pieces.

1

+

1 4

1 2

b. Rewrite the mixed number as an improper fraction and multiply.

5 4

1 2

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Chapter 2 Multiplying and Dividing Fractions

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Spanish

3 ACTIVITY: Buried Treasure Game

Number of Players: 2

Taking turns, each player will

choose a treasure location. roll a number cube as many times as there are blanks in the expression. place the numbers in the blanks to form the largest possible value

for that treasure location. check each other's work. Players then total the values of their treasures (sum of the three expressions). The player with the larger total wins the game.

( (

(

( - =?

( ? =?

? =?

( + =?

+ =?

- =?

4. IN YOUR OWN WORDS How do you multiply a mixed number by a fraction?

Use what you learned about multiplying mixed numbers to complete Exercises 8 ?15 on page 66.

Section 2.4 Multiplying Mixed Numbers

63

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2.4 Lesson

Lesson Tutorials

EXAMPLE 1 Using the Distributive Property

Use

the

Distributive

Property

to

find

1 --

?

2--3.

2 4

( ) 1

--

?

2--3

=

1 --

?

2

+

3 --

2 42

4

Rewrite

2

3 --

as

the

sum

2

+

--3.

4

4

( ) ( ) = --1 ? 2 + --1 ? --3

2

2 4

Use the Distributive Property.

= 1 + --3

8

= 1--3

8

Multiply. Add.

Exercises 4 ?7

Use the Distributive Property to find the product.

1.

2 --

?

1--1

3 2

2. --3 ? 2--1

5 6

3.

1 --

?

4

-- 1

4 5

4.

2 --

?

3

-- 3

7 4

Multiplying Mixed Numbers

Write each mixed number as an improper fraction. Then multiply as you would with fractions.

EXAMPLE 2 Multiplying a Fraction and a Mixed Number

Find --1 ? 2--3.

2 4

Estimate --1 ? 3 = 1 --1

2

2

--1 ? 2 --3 = --1 ? -- 11

2 42 4

Write

2

3 --

as

the

improper

fraction

-- 11.

4

4

=

1 ? 11 -- 2 ? 4

Multiply the numerators and the denominators.

= -- 11, or 1--3

8

8

So, the product is 1 --3.

8

Simplify.

Reasonable? 1--3 1--1 8 2

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Chapter 2 Multiplying and Dividing Fractions

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EXAMPLE 3 Multiplying Mixed Numbers

Find 1--4 ? 3 --2.

5 3

Estimate 2 ? 4 = 8

1--4

?

3--2

=

9 --

?

11 --

5 35 3

=3-- 9 ? 11

5 ? 3 1

= -- 33, or 6 --3

5

5

So, the product is 6 --3.

5

Write

1--4

and

3

2 --

as

improper

fractions.

5

3

Multiply fractions. Divide out the common factor 3.

Simplify.

Reasonable?

6

3 --

8

5

Exercises 8 ?23

Multiply. Write the answer in simplest form.

5.

1 --

?

1--1

3 6

6. 3--1 ? --4

2 9

7. 1--7 ? 2--2

8 5

8. 5--5 ? 2--1

7 10

EXAMPLE 4 Real-Life Application

A city is resurfacing a basketball court. Find the area of the court. Estimate 21 ? 14 = 294

21

1 3

m

13

1 2

m

A = w

=

21

1 --

?

13

1 --

3

2

=

64 --

?

27 --

3 2

32

9

= -- 64 ? 27

1 3?21

= 288

Write the formula for the area of a rectangle.

Substitute 21--1 forand 13--1 for w.

3

2

Write 21--1 and 13--1 as improper fractions.

3

2

Multiply fractions. Divide out common factors.

Simplify.

The area of the court is 288 square meters.

Reasonable? 288 294

9. Find the area of a rectangular air hockey table that is

8--1 feet by 4--3 feet.

4

8

Section 2.4 Multiplying Mixed Numbers

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Spanish

2.4 Exercises

Help with Homework

1. VOCABULARY What is an improper fraction?

2. WRITING Describe how to multiply two mixed numbers.

3. OPEN-ENDED Write two mixed numbers between 3 and 4 that have a product between 9 and 12.

93++4(-+(6-9(3)-=+)9=3()-=1)=

Use the Distributive Property to find the product.

1 4. --1 ? 2 --2

4 7

5. --5 ? 2 --2

6 5

6. --5 ? 4 --1

9 2

Multiply. Write the answer in simplest form.

2

3

8.

1--1

?

2 --

3 3

9.

6

2 --

?

3 --

3 10

10.

2

1 --

?

4 --

2 5

12.

7

1 --

?

2 --

2 3

13.

5 --

?

3

3 --

9 5

14.

3 --

?

1--1

4 3

16. 4 --3 ? --4

8 5

17. --3 ? 2 --5

7 6

18. 1--3 ? 18

10

20. 1--1 ? 6 --3

6 4

21. 2 --5 ? 2 --2

12 3

22. 5 --5 ? 3 --1

7 8

7. --2 ? 5 --5

15 8

11.

3 --

?

3

1 --

5 3

15.

3

3 --

?

2 --

4 5

19. 15 ? 2 --4

9

23. 2 --4 ? 4 --1

5 16

ERROR ANALYSIS Describe and correct the error in finding the product.

24.

4 ? 3 --7 = 12 --7

10

10

( ) 25.

2--1 ? 7--4 = (2 ? 7) + --1 ? --4

2 5

2 5

= 14 + --2 = 14 --2

5

5

26. VITAMIN C A vitamin C tablet contains --1 gram of vitamin C. You take

40

1--1 tablets every day. How many grams of vitamin C do you take every day?

2

27. SCHOOL BANNER A banner is made for a football rally.

a. What is the area of the banner? b. A --1 -foot border is added on each side. What is

4

the new area of the banner?

GO PANTHERS!

1

1 2

ft

4

2 3

ft

66

Chapter 2 Multiplying and Dividing Fractions

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