Holt CA Course 1

4-2 Adding and Subtracting Fractions

NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.Also covered: NS2.4

California Standards

Holt CA Course 1

4-2 Adding and Subtracting Fractions

To add and subtract fractions with like denominators, add or subtract the numerators and keep the common denominator.

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Add. Write the answer in simplest form.

Teacher Example 1A: Adding and Subtracting Fractions with Like Denominators

58

+ 18

58

+ 18

= 5 + 18

Add the numerators and keepthe common denominator.

= 68

= 34 Simplify.

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Subtract. Write the answer in simplest form.

Teacher Example 1B: Adding and Subtracting Fractions with Like Denominators

911

– 411

911

–4

11= 9 – 4

11Subtract the numerators andkeep the common denominator.

The answer is in the simplestform.

= 5 11

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Add. Write the answer in simplest form.

Student Practice 1A:

56

+ 16

56

+ 16

= 5 + 16

Add the numerators and keepthe common denominator.

= 66

= 1 Simplify.

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Subtract. Write the answer in simplest form.

Student Practice 1B:

710

– 410

710

–4

10= 7 – 4

10Subtract the numerators andkeep the common denominator.

The answer is in the simplestform.

= 3 10

Holt CA Course 1

4-2 Adding and Subtracting Fractions

To add or subtract fractions with different denominators, you must rewrite the fractions with a common denominator.

Two Ways to Find a Common Denominator

Method 1: Multiply the denominators.

Method 2: Find the LCM (least common multiple) of the denominators.

Holt CA Course 1

4-2 Adding and Subtracting Fractions

The LCM of two denominators is the least common denominator (LCD) of the fractions.

Helpful Hint

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Subtract. Write the answer in simplest form.

Teacher Example Example 2A: Adding and Subtracting Fractions with Unlike Denominators

34

– 23

34

– 23

= 3 34 3

– 2 43 4

Use Method 1: Multiply the denominators.

Write equivalent fractions using a common denominator.

Subtract.

= 912

– 812

= 112

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Add. Write the answer in simplest form.

18

+ 35

Use Method 2: The LCM of the denominators is 40.

Write equivalent fractions using a common denominator.

= Add.

18

+35

= 1 58 5

+ 3 85 8

Teacher Example 2B: Adding and Subtracting Fractions with Unlike Denominators

= + 2440

540

2940

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Add. Write the answer in simplest form.

Teacher Example 2C: Adding and Subtracting Fractions with Unlike Denominators

56

+ 78

56

+ 78

= 5 46 4

+ 7 38 3

Use Method 2: The LCM of the denominators is 24.

= 2024

+ 2124

Write equivalent fractions using a common denominator.

= 4124

=1 1724

Add. Then simplify.

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Subtract. Write the answer in simplest form.

Student Practice 2A:

35

– 12

35

– 12

= 3 25 2

– 1 52 5

Use Method 1: Multiply the denominators.

Write equivalent fractions using a common denominator.

Subtract.

= 610

– 510

= 110

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Add. Write the answer in simplest form.

35

+ 12

Use Method 1: Multiply the denominators.Write equivalent fractions using a common denominator.

= Add. Then simplify.

35

+12

= 3 25 2

+ 1 52 5

Student Practice 2B:

= + 510

610

1110

= 1 110

Holt CA Course 1

4-2 Adding and Subtracting Fractions

Add. Write the answer in simplest form.

Student Practice 2C:

25

+ 56

25

+ 56

= 2 65 6

+ 5 56 5

Use Method 2: The LCM of the denominators is 30.

= 1230

+ 2530

Write equivalent fractions using a common denominator.

= 3730

Add. Then simplify.= 1 730

Holt CA Course 1

4-2 Adding and Subtracting FractionsTeacher Example 3: Astronomy Application

1 62 6

– 1 112 1

Use Method 2: The LCM of the denominators is 12.

Write equivalent fractions using a common denominator.

Subtract.

12

– = 112

= 612

– 112

= 512

In one Earth year, Jupiter completes about

of its orbit around the Sun, while Mars

completes about of its orbit. How much more

of its orbit does Mars complete than Jupiter?

12

112

Mars completes more of its orbit than Jupiter does. 512

Holt CA Course 1

4-2 Adding and Subtracting FractionsStudent Example 3:

1 62 6

– 5 112 1

The LCM of the denominators is 12.

Write equivalent fractionsusing a common denominator.

Subtract.

12

– = 512

= 612

– 512

= 112

It takes Michelle hour to drive to work. It

takes Luke hour to drive to work. How much

longer does it take Luke to drive to work?

12

512

It takes Luke hour longer to drive to work.112