Holt CA Course 1

4-6 Solving Equations Containing Fractions

AF1.1 Write and solve one-step linear equations in one variable.Also covered: NS2.1, NS2.2,

NS2.4

California Standards

Holt CA Course 1

4-6 Solving Equations Containing Fractions

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

Holt CA Course 1

4-6 Solving Equations Containing Fractions

Solve. Write the answer in simplest form.

Example 1A: Solving Equations by Adding or Subtracting

x – 37

= 57

x – 37

= 57

x – 37

+ 37

= 57

+ 37

x = 87

=1 17

Simplify.

37

Since is subtracted from x, 37

add to both sides.

Holt CA Course 1

4-6 Solving Equations Containing Fractions

Solve. Write the answer in simplest form.

Example 1B: Solving Equations by Adding or Subtracting

512

+ t =38

38

+ t = 512

Find a common denominator.

Subtract.

38

+ t – =5

12–

38

38

t = 1024

– 924

t = 124

Since is added to t, 38

38

subtract from both sides.

Holt CA Course 1

4-6 Solving Equations Containing Fractions

Solve. Write the answer in simplest form.

Example 2A: Solving Equations by Multiplying

38

x = 14

38

x =83

14

83

2

1

=x 23

Multiply by the reciprocal of .38

Then simplify.

38

= 14

x =

To undo multiplying by

Caution!38

, you can divide by 38

or multiply by its reciprocal, 83 .

Holt CA Course 1

4-6 Solving Equations Containing Fractions

Additional Example 2B: Solving Equations by Multiplying

4y = 8989

4y = 14

89

141

2

y = 29

4y = Multiply by the reciprocal of 4.

Then simplify.

Solve. Write the answer in simplest form.

Holt CA Course 1

4-6 Solving Equations Containing FractionsExample 3: Physical Science Application

The amount of copper in brass is of the total weight. If a

sample contains 4 ounces of copper, what is the total

weight of the sample?

34

15

Let w represent the total weight of the sample.34

w = 4 15

34

w 43

= 4 15 4

3

w = 215

43

7

1

w = 285

or 5 35

Write an equation.

Multiply by the reciprocal of 34

·

Write 4 15

as an improperfraction.

Then simplify.

The sample weighs 535

ounces.

Holt CA Course 1

4-6 Solving Equations Containing Fractions

Solve. Write the answer in simplest form.

Check It Out! Example 1

x – 38

= 78

x – 38

= 78

x – 38

+ 38

= 78

+ 38

x = 10 8

= 1 14

Simplify.

Since is subtracted from x, add to both sides.

38

38

Holt CA Course 1

4-6 Solving Equations Containing Fractions

Check It Out! Example 2

3y = 6767

y = 13

67

131

2

y = 27

3y =

3

Multiply by the reciprocal of 3.

Then simplify.

Solve. Write the answer in simplest form.

Holt CA Course 1

4-6 Solving Equations Containing Fractions

The amount of copper in zinc is of the total weight. If a

sample contains 5 ounces of copper, what is the total

weight of the sample?

Check It Out! Example 314

13

Let w represent the total weight of the sample.14

w = 5 13

14

w 41

= 5 13

41

w = 163

41

w = 643

or 21 13

Write an equation.

Multiply by the reciprocal of 14

·

Write 5 13

as an improperfraction.

Multiply.

The sample weighs 2113

ounces.