This document is a lesson on solving fraction equations by multiplying and dividing fractions. It includes examples of solving equations such as 3x = 2/3 by multiplying both sides by the reciprocal. It also includes a word problem example where Dexter used 12 cups of powdered milk, which was 2/3 of the recipe amount, to solve for the total cups in the recipe. The document provides step-by-step work and explanations for setting up and solving these fraction equations.

1. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division5-10
Solving Fraction Equations:
Multiplication and Division
Course 1
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Warm UpWarm Up

2. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Warm Up
Solve.
1. x – 5 = 17
2. 5x = 125
3. x + 12 = 86
4. 9x = 108
x = 22
x = 25
x = 74
x = 12

3. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
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

4. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Learn to solve equations by multiplying
and dividing fractions.

5. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Dividing by a number is the same as multiplying
by its reciprocal.
Remember!

6. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Additional Example 1A: Solving Equations by
Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
j = 25
3
5
__
j ÷ = 25 ÷
3
5
__ 3
5
__ 3
5
__
j • = 25 •
3
5
__ 5
3
__ 5
3
__
j =
25 • 5
1 • 3
_____
j = 25 •
5
3
__
j = , or 41
125
3
___ 2
3
__
Divide both sides of the equation by .
3
5
__
Multiply by , the reciprocal of .
3
5
__5
3
__

7. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Additional Example 1B: Solving Equations by
Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
7x =
2
5
__
7x
1
__ 2
5
__ 1
7
__1
7
__
• = •
x =
2 • 1
5 • 7
____
x =
2
35
__
Multiply both sides by the reciprocal
of 7.
The answer is in simplest form.

8. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Additional Example 1C: Solving Equations by
Multiplying and Dividing
Solve each equation. Write the answer in simplest form.
= 6
5y
8
__
5y
8
__ 6
1
__ 5
8
__5
8
__
÷ = ÷
y = , or 9
48
5
__
Divide both sides by .
5
8
__
5y
8
__ 6
1
__ 8
5
__8
5
__
• = •
3
5
__
5
8
Multiply by the reciprocal of .
__

9. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Check It Out: Example 1A
Solve each equation. Write the answer in simplest form.
j = 19
3
4
__
j ÷ = 19 ÷
3
4
__ 3
4
__ 3
4
__
j • = 19 •
__3
4
__ 4
3
4
3
__
j =
19 • 4
1 • 3
_____
4
j = 19 •
3
__
76___ 1
3
j = , or 25
3
__
Divide both sides of the equation by .
3
4
__
Multiply by , the reciprocal of .
3
4
__4
3
__

10. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Check It Out: Example 1B
Solve each equation. Write the answer in simplest form.
3x =
1
7
__
3x
1
__ 1
7
__ 1
3
__1
3
__
• = •
x =
1 • 1
7 • 3
____
x =
1
21
__
Multiply both sides by the reciprocal
of 3.
The answer is in simplest form.

11. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Check It Out: Example 1C
Solve each equation. Write the answer in simplest form.
= 4
6y
7
__
6y
7
__ 4
1
__ 6
7
__6
7
__
÷ = ÷
y = , or 4
28
6
__
Divide both sides by .
Multiply by the reciprocal of .
6
7
__
6y
7
__ 4
1
__ 7
6
__7
6
__
• = •
2
3
__
6
7
__

12. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Additional Example 2: Problem Solving Application
2
3
__
Dexter makes of a recipe, and he uses 12
cups of powdered milk. How many cups of
powdered milk are in the recipe?

13. Course 1
5-10
Solving 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:
2
3
__
• He makes of the recipe.
• He uses 12 cups of powdered milk.

14. Course 1
5-10
Solving 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.
2
3
__12 = x
Additional Example 2 Continued

15. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Solve33
2
3
__12 = x
12 • = x •
3
2
__ 2
3
__ 3
2
__
12
1
__ 3
2
__• = x
6
1
18 = x
There are 18 cups of powdered milk in the recipe.
Multiply both sides by , the
reciprocal of .
3
2
__
2
3
__
Simplify. Then multiply.
Additional Example 2 Continued

16. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Look Back44
Check 12 = x
2
3
__
2
3
__12 =
?
(18)
36
3
__12 =
?
12 = 12
?
Substitute 18 for x.
Multiply and simplify.
18 is the solution.
Additional Example 2 Continued
12
1

17. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Check It Out: Example 2
2
5
__
Nick makes of a recipe, and he uses 8
cups of wheat flour. How many cups of
wheat flour are in the recipe?

18. Course 1
5-10
Solving 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.
2
5
__
List the important information:
• He makes of the recipe.
• He uses 8 cups of wheat flour.

19. Course 1
5-10
Solving 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.
2
5
__8 = y
Check It Out: Example 2 Continued

20. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Solve33
2
5
__8 = y
8 • = y •
5
2
__ 2
5
__ 5
2
__
8
1
__ 5
2
__• = y
4
1
20 = y
There are 20 cups of wheat flour in the recipe.
Multiply both sides by , the
reciprocal of .
5
2
__
2
5
__
Simplify. Then multiply.
Check It Out: Example 2 Continued

21. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Look Back44
Check 8 = y
2
5
__
2
5
__8 =
?
(20)
40
5
__8 =
?
8 = 8
?
Substitute 20 for y.
Multiply and simplify.
20 is the solution.
Check It Out: Example 2 Continued
8
1

22. Course 1
5-10
Solving Fraction Equations:
Multiplication and Division
Lesson Quiz
Solve 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?
1
8
__ 1
4
__
3
7
__ y
7
__
1
4
__
x = 161
24
__x =
98
3
__ 2
3
__x = or 32 y = 63
12