5-7Solving Fraction Equations: Multiplication and Division
Learn to solve equations by multiplying and dividing fractions.
5-7Solving Fraction Equations: Multiplication and Division
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__
5-7Solving Fraction Equations: Multiplication and Division
Additional Example 1B: Solving Equations by Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
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.
5-7Solving Fraction Equations: Multiplication and Division
Additional Example 1C: Solving Equations by Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
= 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 .
__
5-7Solving Fraction Equations: Multiplication and Division
Check It Out: Example 1A
Solve each equation. Write the answer in simplest form.
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__
5-7Solving Fraction Equations: Multiplication and Division
Check It Out: Example 1B
Solve each equation. Write the answer in simplest form.
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.
5-7Solving Fraction Equations: Multiplication and Division
Check It Out: Example 1C
Solve each equation. Write the answer in simplest form.
= 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__
5-7Solving Fraction Equations: Multiplication and Division
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?
5-7Solving Fraction Equations: Multiplication and Division
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.
5-7Solving Fraction Equations: Multiplication and Division
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
Additional Example 2 Continued
5-7Solving Fraction Equations: Multiplication and Division
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.
Additional Example 2 Continued
5-7Solving Fraction Equations: Multiplication and Division
Look Back44
Check 12 = x23__
23__12 =
? (18)
363__12 =
?
12 = 12?
Substitute 18 for x.
Multiply and simplify.
18 is the solution.
Additional Example 2 Continued
12
1
5-7Solving Fraction Equations: Multiplication and Division
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?
5-7Solving Fraction Equations: Multiplication and Division
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.
5-7Solving Fraction Equations: Multiplication and Division
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
Check It Out: Example 2 Continued
5-7Solving Fraction Equations: Multiplication and Division
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.
Check It Out: Example 2 Continued
5-7Solving Fraction Equations: Multiplication and Division
Look Back44
Check 8 = y25__
25__ 8 =
? (20)
405__ 8 =
?
8 = 8?
Substitute 20 for y.
Multiply and simplify.
20 is the solution.
Check It Out: Example 2 Continued
8
1