5-7 Solving Fraction Equations: Multiplication and Division Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

5-7Solving Fraction Equations: Multiplication and Division

Warm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes


Warm UpSolve.

1. x – 5 = 17

2. 5x = 125

3. x + 12 = 86

4. 9x = 108

x = 22

x = 25

x = 74

x = 12


Problem of the Day

Stephen forgot his locker number, but he remembered that the sum of the digits is 11 and that the digits are all odd numbers. The locker numbers are from 1 to 120. What is Stephen’s locker number?

119


Learn to solve equations by multiplying and dividing fractions.


Dividing by a number is the same as multiplying by its reciprocal.

Remember!

5-7Solving Fraction Equations: Multiplication and DivisionAdditional Example 1A: Solving Equations by

Multiplying and Dividing

Solve each equation. Write the answer in simplest form.

j = 25 35__

j ÷ = 25 ÷ 35__ 3

5__ 3

5__

j • = 25 • 35__ 5

3__ 5

3__

j = 25 • 51 • 3_____

j = 25 • 53__

j = , or 41125

3___ 2

3__

Divide both sides of the equation by .

35__

Multiply by , the reciprocal of .

35__5

3__


Additional Example 1B: Solving Equations by Multiplying and Dividing


7x = 25__

7x1__ 2

5__ 1

7__1

7__• = •

x =

2 • 15 • 7____

x =

235__

Multiply both sides by the reciprocal of 7.

The answer is in simplest form.


Additional Example 1C: Solving Equations by Multiplying and Dividing


= 65y8__

5y8__ 6

1__ 5

8__5

8__÷ = ÷

y = , or 9 485__

Divide both sides by .

58__

5y8__ 6

1__ 8

5__8

5__• = •

35__

58Multiply by the reciprocal of .

__


Check It Out: Example 1A


j = 19 34__

j ÷ = 19 ÷ 34__ 3

4__ 3

4__

j • = 19 • __3

4__ 4

343__

j = 19 • 41 • 3_____

4j = 19 • 3__

76___ 13

j = , or 253

__

Divide both sides of the equation by .

34__

Multiply by , the reciprocal of .

34__4

3__


Check It Out: Example 1B


3x = 17__

3x1__ 1

7__ 1

3__1

3__• = •

x =

1 • 17 • 3____

x =

121__

Multiply both sides by the reciprocal of 3.

The answer is in simplest form.


Check It Out: Example 1C


= 46y7__

6y7__ 4

1__ 6

7__6

7__÷ = ÷

y = , or 4 286__

Divide both sides by .

Multiply by the reciprocal of .

67__

6y7__ 4

1__ 7

6__7

6__• = •

23__

67__


Additional Example 2: Problem Solving Application

23__

Dexter makes of a recipe, and he uses

12 cups of powdered milk. How many

cups of powdered milk are in the recipe?


Additional Example 2 Continued

1 Understand the Problem

The answer will be the number of cups of powdered milk in the recipe.

List the important information:

23__• He makes of the recipe.

• He uses 12 cups of powdered milk.


2 Make a Plan

You can write and solve an equation. Let x represent the number of cups in the recipe.

He uses 12 cups, which is two-thirds of the amount of the recipe.

23__12 = x



Solve3

23__12 = x

12 • = x •32__ 2

3__ 3

2__

121__ 3

2__• = x

6

118 = x

There are 18 cups of powdered milk in the recipe.

Multiply both sides by , the

reciprocal of .

32__

23__

Simplify. Then multiply.



Look Back4

Check 12 = x23__

23__12 =

? (18)

363__12 =

?

12 = 12?

Substitute 18 for x.

Multiply and simplify.

18 is the solution.


12

1


Check It Out: Example 2

25__Nick makes of a recipe, and he

uses 8 cups of wheat flour. How

many cups of wheat flour are in the

recipe?


Check It Out: Example 2 Continued

1 Understand the Problem

The answer will be the number of cups of wheat flour in the recipe.

25__

List the important information:

• He makes of the recipe.

• He uses 8 cups of wheat flour.


2 Make a Plan

You can write and solve an equation. Let y represent the number of cups in the recipe.

He uses 8 cups, which is two-fifths of the amount of the recipe.

25__8 = y



Solve3

25__ 8 = y

8 • = y •52__ 2

5__ 5

2__

81__ 5

2__• = y

4

120 = y

There are 20 cups of wheat flour in the recipe.

Multiply both sides by , the

reciprocal of .

52__

25__

Simplify. Then multiply.



Look Back4

Check 8 = y25__

25__ 8 =

? (20)

405__ 8 =

?

8 = 8?

Substitute 20 for y.

Multiply and simplify.

20 is the solution.


8

1


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson QuizSolve each equation. Write the answer in simplest form.

1. 3x = 2. x = 4

3. x = 14 4. = 9

5. Rebecca used 3 pt of paint to paint of the

trim in her bedroom. How many pints will Rebecca

use for the trim in the entire bedroom?

18__ 1

4__

37__ y

7__

14__

x = 16124__x =

983__ 2

3__x = or 32 y = 63

12


1. Solve the equation and identify the answer in the simplest form.

A. C.

B. D.




A. x = 5 C. x = 25

B. x = 10 D. x = 50




A. C.

B. D.




A. y = 72 C.

B. y = 17 D.



5. Lou is learning to paint pottery. He used 3

pints of paint to paint of a pot. How

many pints will Lou use for the entire pot?

A. C. 3 pt

B. D. 7 pt


Documents

5-7 Solving Fraction Equations: Multiplication and Division Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day