5-7 Solving Fraction Equations: Multiplication and Division Learn to solve equations by multiplying and dividing fractions

$Page 1: 5-7 Solving Fraction Equations: Multiplication and Division Learn to solve equations by multiplying and dividing fractions$
5-7Solving Fraction Equations: Multiplication and Division

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

11 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.


22 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



Solve33

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 Back44

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

11 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.


22 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



Solve33

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 Back44

Check 8 = y25__

25__ 8 =

? (20)

405__ 8 =

?

8 = 8?

Substitute 20 for y.

Multiply and simplify.

20 is the solution.


8

1

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5-7 Solving Fraction Equations: Multiplication and Division Learn to solve equations by multiplying and dividing fractions