1-4 Adding and Subtracting with Unlike Denominators

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

1-4 Adding and Subtracting with Unlike Denominators

Warm UpAdd 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

1-4 Adding and Subtracting with Unlike Denominators

Problem of the Day

The least common multiple of 6 and a number is 24. What is the other number?

8 or 24

1-4 Adding and Subtracting with Unlike Denominators

Learn to add and subtract fractions with unlike denominators.

1-4 Adding and Subtracting with Unlike Denominators

Two hikers on the Appalachian Trail are 5 from the trail ahead. The hikers walk 2 miles before taking a break. They then hike another 1 miles before taking a second break. How many more miles do they have to hike before reaching the summit?

3 4

1 2

1 8

1-4 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).

1-4 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:

1-4 Adding and Subtracting with Unlike Denominators

1 61 – 1 5

8 List the multiples of each denominator and find the LCD

Write as improper fractions.

Multiples of 6: 6; 12; 18; 24; 30

Multiples of 8: 8; 16; 24; 32

Rewrite with a common denominator.

13 8

–7 6

4 4

3 3

11 24

= – 39 24–28

24

Multiply by fractions equal to 1.

Simplify.

–7 6

13 8

B.

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

Add or Subtract. Method 2:

1-4 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

Check It Out: Example 1A

Add or Subtract. Method 1:

=15 24

+8 24

A.

5 8

+1 3

8 8

3 3

1-4 Adding and Subtracting with Unlike Denominators

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

Rewrite with a common denominator.

Multiply by fractions equal to 1.

Simplify.

3 4+

13 6

3 4+

13 6

2 2

33

B.

11 12

= 235 12=9

12+26 12

Check It Out: Example 1B

Add or Subtract. Method 2:

1-4 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 t.5 6

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

4 5

–5 6

5 5

6 6

1-4 Adding and Subtracting with Unlike Denominators

Check It Out: Example 2

Multiply by fractions equal to 1.

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

1-4 Adding and Subtracting with Unlike DenominatorsAdditional 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.

, 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

1-4 Adding and Subtracting with Unlike Denominators

Check It Out: Example 3

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 foot left.

5 6

81 12

144 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

1-4 Adding and Subtracting with Unlike Denominators

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

1-4 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

–2 1 15

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

12

2 in.3 4

1-4 Adding and Subtracting with Unlike Denominators

1. Add.

+

A. C. 1

B. D. 1

Lesson Quiz for Student Response Systems

1 2

3 4

1 3

1 2

7 12

1 6

1-4 Adding and Subtracting with Unlike Denominators

2. Subtract.

8 – 6

A. 2 C. 3

B. 2 D. 3

Lesson Quiz for Student Response Systems

1 2

3 4

1 4

3 4

1 4

1-4 Adding and Subtracting with Unlike Denominators

3. Add or subtract.

+ –3

A. –2 C. 2

B. –2 D. 2

Lesson Quiz for Student Response Systems

11

181 3

1 3

4 9

8 9

1 2

1-4 Adding and Subtracting with Unlike Denominators

4. Evaluate 1 – x for x = .

A. 1 C.

B. D.

Lesson Quiz for Student Response Systems

13

14

11 14

9 14

1 7

5 14

1-4 Adding and Subtracting with Unlike Denominators

5. A pine tree is 20 feet 3 inches tall.

Another pine tree is 20 feet 5 inches tall.

How much taller is the second pine tree than the first?

A. 2 in. C. 3 in.

B. 2 in. D. 3 in.

Lesson Quiz for Student Response Systems

1 2

1 4

1 2

1 4 3

4

1 4