1. The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to isolate the variable on one side of the equation.

2. Additional Example 1A: Solving Equations by Adding or Subtracting
Solve. Write the answer in simplest form. 3 7 5 7
x – =
x – 3 7 = 5
Use the Addition Property of Equality.
x – 3 7 + = 5 x = 8 7 1
Add.

3. Additional Example 1B: Solving Equations by Adding or Subtracting
Solve. Write the answer in simplest form. 4 9 -1 2
+ r = 4 9 + r -1 2 =
Use the Subtraction Property of Equality. 4 9 r 4 9 -1 2 4 9 + – = – r -9 18 8 18 =
Find a common denominator. – 17 18 r = –
Subtract.
You can also isolate the variable r by adding the opposite of
Helpful Hint 4 9 , – 4 9 ,
to both sides.

4. Check It Out: Example 1A 3 8 7 8
x – =
x – 3 8 = 7 x– +
x = 10
= 1 1 4 5

5. Check It Out: Example 1B 3 8 5 6
x – =
x – 3 8 = 5 6 + x 29 24 1 20 9

6. Recall that the product of a nonzero number and its reciprocal is 1
Recall that the product of a nonzero number and its reciprocal is 1.This is called the Multiplicative Inverse Property.
You can use the Multiplicative Inverse Property to solve multiplication equations that contain fractions and whole numbers.

7. Additional Example 2A: Solving Equations by Multiplying
Solve. Write the answer in simplest terms. 3 8 1 4 x = 3 8 = 1 4 x 3 8
Multiply by the reciprocal of . 2 3 8 . 8 3 1 4 . 8 3 x =
Then simplify. 1 2 3 x =
Caution!
To undo multiplying by 3 8 3 8
, you can divide by 8 3
or multiply
by its reciprocal, .

8. Additional Example 2B: Solving Equations by Multiplying
Solve. Write the answer in simplest terms. 8 9
4y = 8 9
4y =
Multiply by the reciprocal of 4. 2 4 y . 1 4 8 9 = . 1 4
Then simplify. 1 2 9
y =

9. Check It Out: Example 2A 1 2 5 8 – x = 1 – 2 x = 4 5 8
x =

10. Check It Out: Example 2B 3 7 6 y = 1 6 y = 3 7 2
y = 14

11. Check It Out: Example 2C 2 3 3 4 – z = 1 – 3 2 z = 4
z = 9 8

12. Check It Out: Example 2D 8 9 – 4 p = 1 4 p = 2 8 9
p = –

13. Additional Example 3: Food Application
Melissa made a fruit salad using a total of 5 pounds of various fruits. She used 1 pounds of grapes, and she used equal portions of 5 other fruits in her salad. What weight of each of these fruits did she use? 1 4 1 2 1 2
f = 5 4
Write an equation. Let f represent the amount of each fruit. 1 2
1 – f = 5 – 1 4
Subtract 1 from both sides. 1 2
Think: 5 – 1 = 4 – 1 . 1 4 2 5
5f = 3 3 4
5f  = 3  3 4 1 5
Multiply both sides by the reciprocal of 5 to isolate f.
f =  15 4 1 5 3 4
Rewrite 3 as an improper fraction.
f = 15 20 or 3 4
Multiply and simplify.
She used of a pound of each of the 5 other fruits. 3 4

14. Check It Out: Example 3
A salad bar in a restaurant contains pounds of vegetables. There are pounds of greens, and there are equal amounts of onions, bell peppers, celery, carrots, and cucumbers. How much of each of these vegetables does the salad bar contain? 5 6 10 1 3 5 6 10 1 3 = + x 65 – 20

15. Check It Out: Example 3 Continued1 5 45 6 9 = x 3 2
pounds

16. Solve. Write each answer in simplest form. 1. 2. 3. 4.
Lesson Quiz
Solve. Write each answer in simplest form. 1. 2. 3. 4. 3 8 5 8
x – = 1 7 16 19 32 5 32
y + = x 4 3 7 12 7 5
or 1 = 3 4 1 3 16 9 7
or 1 x = 1
5. During the week, Marissa ate some apples from a basket. She left 20 apples. This was five-eights the number of apples she had bought earlier in the week. How many apples did she buy? 32