Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators55 Adding and Subtracting Fractions with

Unlike Denominators

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

Warm UpAdd or subtract.

1 + 2 5 21. 4

5

2. 7 123 – 2

3. 6.5 x 1.2

4. .72 ÷ 0.09

7.8

8

3 5

11 12

1 3 1

55 Adding and Subtracting with Unlike Denominators

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

Least common multiple: the least whole number that is a multiple of 2 or more given numbers

Least common denominator (LCD): the least common multiple of two or more denominators.

Vocabulary

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

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?

1 3

2 5

1 2

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

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.

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

Find a common denominator: 8(7)=56.

2 7

+1 8

Multiply by fractions equal to 1.

Rewrite with a common denominator.Simplify

Additional Example 1A: Adding and Subtracting Fractions with Unlike Denominators

2 7

+1 8

7 7

8 8

23 56

=16 56

+7 56

A.

Add or Subtract. Method 1:

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

The least common multiple of two numbers is the smallest number other than zero that is a multiple of the two numbers.

Remember!

1 61 +

5 8 List the multiples of each

denominator and find the LCD

Write as an improper fraction.

Multiples of 6: 6; 12; 24; 30

Multiples of 8: 8; 16; 24; 32

Rewrite with a common denominator.

5 8+

7 6

4 4

3 3

43 24=

15 24+

28 24

19 24= 1

Multiply by fractions equal to 1.

Simplify.

5 8+

7 6

B.

Additional Example 1B: Adding and Subtracting Fractions with Unlike Denominators

Add or Subtract. Method 2:

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

Find a common denominator 3(8)=24.

5 8

+1 3

Multiply by fractions equal to 1.

Rewrite with a common denominator.

23 24

Try This: Example 1A

Add or Subtract. Method 1:

=15 24

+8 24

A.

5 8

+1 3

8 8

3 3

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

1 62 +

3 4 List the multiples of each

denominator and find the LCD

Multiples of 6: 6; 12; 24; 30

Multiples of 4: 4; 8; 12; 16

Rewrite with a common denominator.

Multiply by fractions equal to 1.

Simplify.

B.

Try This: Example 1B

Add or Subtract. Method 2:

3 4+

1 6

2 2

332

11 12=9

12+2

122 2

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

Evaluate t – for t = .

Additional Example 2: Evaluating Expressions with Rational Numbers

4 5

–5 6

24 30

–25 30

1 30

=

Multiply by fractions equal to 1.

4 5

5 6

Substitute for n.5 6

Rewrite with a common denominator: 6(5) = 30.

4 5

–5 6

5 5

6 6

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

Additional Example 3: Consumer Application

Subtract both amounts from 36 to find the amount of ribbon left.Write as improper fractions. The LCD is 8.

36 – 12 – 13 7 8

3 4

Rewrite with a common denominator. Simplify. 9 3

8There will be 9 inches left.

3 8

Two dancers are making necklaces from ribbon for their costumes. They need pieces measuring 13 inches and 12 inches. How much ribbon will be left over after the pieces are cut from a 36-inch length?

7 8

3 4

– 12 – 13 7 8

8 835

6 8

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

Add or subtract.

1. +5 14

1 7

13 16

2.

12

2 38 1– 7

1 6

3. –2+ 3 5

2 3

4. Evaluate – n for n = . 138 9 16

Lesson Quiz: Part 1

–2 1 15

12

Pre-Algebra

3-5 Adding and Subtracting with Unlike Denominators

Lesson Quiz: Part 2

Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy?

5.3 4

12

2 in.3 4