Adding and Subtracting with Unlike

Denominators

- 3.5

Warm Up

Add or subtract.

2 5

3 5

1.

1

7 12

11 12

2.

3 2

3. 6.5 1.2

5.3

4. 3.4 0.9

2.5

Learn to add and subtract fractions with unlike

denominators.

Vocabulary

least common denominator (LCD)

1 3

A pattern for a double-circle skirt requires 9

yards of 45-inch-wide material. To add a ruffle

takes another 2 yards. If the total amount of

material for the skirt and ruffle are cut from a

bolt of fabric 15 yards long, how much fabric

is left?

2 5

1 2

To solve this problem, add and subtract rational

numbers with unlike denominators. First find a

common denominator using one of the following

methods

Method 1 Find a common denominator by

multiplying one denominator by the other

denominator.

Method 2 Find the least common denominator

(LCD) the least common multiple of the

denominators.

Example Adding and Subtracting Fractions with

Unlike Denominators

Add or Subtract. Method 1

Find a common denominator 8(7)56.

2 7

1 8

A.

Multiply by fractions equal to 1.

Rewrite with a common denominator. Simplify

Example Adding and Subtracting Fractions with

Unlike Denominators

Add or Subtract. Method 2

Write as an improper fraction.

1 6

5 8

B.

1

List the multiples of each denominator and find

the LCD

Multiply by fractions equal to 1.

Rewrite with a common denominator.

Simplify.

Try This

Add or Subtract. Method 1

Find a common denominator 3(8)24.

5 8

1 3

A.

Multiply by fractions equal to 1.

Rewrite with a common denominator.

Try This

Add or Subtract. Method 2

Write as an improper fraction.

1 6

3 4

B.

2

List the multiples of each denominator and find

the LCD

Multiply by fractions equal to 1.

Rewrite with a common denominator.

Simplify.

Example Evaluating Expressions with Rational

Numbers

4 5

5 6

Evaluate t for t .

Multiply by fractions equal to 1.

Rewrite with a common denominator 6(5) 30.

Try This

5 9

7 12

Evaluate h for h .

Multiply by fractions equal to 1.

Rewrite with lowest common denominator (36).

Simplify.

Example Consumer Application

Subtract both amounts from 36 to find the amount

of ribbon left.

Write as improper fractions. The LCD is 8.

Rewrite with a common denominator.

Simplify.

Try This

Subtract both amounts from 12 to find the amount

of board left.

Write as improper fractions. The LCD is 12.

Rewrite with a common denominator.

Simplify.

Lesson Quiz Part 1

Add or subtract.

5 14

1 7

1.

12

2 3

2.

8

1

3 5

2 3

3.

2

38

9 16

4. Evaluate n for n .

1

Lesson Quiz Part 2

12

Robert is 5 feet 6 inches tall. Judy is 5 feet

3 inches tall. How much taller is Robert than

Judy?

5.

3 4