adding and subtracting with unlike denominators 3.5

Adding and Subtracting with Unlike Denominators

3.5

Add or subtract.

1 + – 1 5 11. 2

5

2. 7 123 – 2

3. 6.5 + –1.2

4. 3.4 – 0.9

5.3

2.5

3 5

11 12

1 3 1

Warm Up

Learn to add and subtract fractions with unlike denominators.

least common denominator (LCD)

Vocabulary

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

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.

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

2 7

+1 8

Multiply by fractions equal to 1.

Rewrite with a common denominator.Simplify

2 7

+1 8

7 7

8 8

23 56

=16 56

+7 56

A.

Add or Subtract. Method 1:

Example: Adding and Subtracting Fractions 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


Simplify.

5 8+

7 6

B.


Example: Adding and Subtracting Fractions with Unlike Denominators

Find a common denominator 3(8)=24.

5 8

+1 3



23 24


=15 24

+8 24

A.

5 8

+1 3

8 8

3 3

Try This

1 62 +

3 4 List the multiples of each

denominator and find the LCD

Write as an improper fraction.

Multiples of 6: 6; 12; 24; 30

Multiples of 4: 4; 8; 12; 16



Simplify.

3 4+

13 6

3 4+

13 6

2 2

33

B.

11 12

= 235 12=9

12+26 12


Try This

Evaluate t – for t = .

4 5

–5 6

24 30

–25 30

1 30

=


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

Example: Evaluating Expressions with Rational Numbers

Evaluate – h for h = .


5 9

–7 12

Substitute for h.–7 12

Rewrite with lowest common denominator (36).

–7 12–

5 9

7 12+5

9=

Simplify.41 36 or 1 5

36

21 36+20

36

–7 12–5

9

7 12+5

9

7 12+5

94 4

3 3

Try This

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.

, or 9 3 8

75 8 There will be 9 inches left.

3 8

103 8

288 8

– – 110 8

103 8

55 4

288 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

Example: Consumer Application

Subtract both amounts from 12 to find the amount of board left.Write as improper fractions. The LCD is 12.

12 – 6 – 4 3 4

5 12

Rewrite with a common denominator. Simplify.

, or 5 6

10 12 There will be inches left.

5 6

81 4144 12

– – 53 12

27 4 53 12

144 12 – –

Fred and Jose are building a tree house. They need to cut a 6 foot piece of wood and a 4 foot piece of wood from a 12 foot board. How much of the board will be left?

5 12

3 4

Try This

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

–2 1 15

12

Lesson Quiz: Part 1

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

Lesson Quiz: Part 2

adding and subtracting with unlike denominators 3.5

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