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3.3

Adding and Subtracting Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 22Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Adding Unlike Fractions

Adding or Subtracting Unlike Fractions

Step 1: Find the LCM of the denominators of the fractions. This number is the least common denominator (LCD).

Step 2: Write each fraction as an equivalent fraction whose denominator is the LCD.

Step 3: Add or subtract the like fractions.Step 4: Write the sum or difference in simplest form.

Martin-Gay, Basic Mathematics, 4e 33Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Adding Unlike Fractions

Step ExampleStep 1: Find the LCM of the denominators of the fractions. This number is the least common denominator (LCD).Step 2: Write each fraction as an equivalent fraction whose denominator is the LCD.

Step 3: Add or subtract the like fractions.

Step 4: Write the sum or difference in simplest form.

31

21

Multiples of 2: 2, 4, 6, 8, 10, …

Multiples of 3: 3, 6, 9, 12, 15, …

22

31

33

21

65

623

62

63

65

is in its simplest form.

2321

3231

62

63

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Example

Add:

Step 1: The LCD of the denominators is 15.

Step 2:

Step 3:

Step 4: The answer is in simplest form.

2 85 15

323

2 65 5 15

2 65 15

8 8 1415 15 15

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Example

Add:

The LCD of the denominators is 24.

2 13 8

2 1 2 13 8 3 8

16 324 2419

8 38 3

Simpl2

est form4

.

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Step Example

Step 1: Write the prime factorization of each number.

Step 2:

Step 3:

Prime factorization for 6: 2, 3Prime factorization for 18: 2, 3, 3

332 LCM 18

P 192

Practice Problem 1

2, 3 3

183

61 Add

183

33

61

183

183

18

33

186

31

Adding Unlike Fractions

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Step Example

Step 1: Write the prime factorization of each number.

Step 2:

Step 3:

Prime factorization for 6: 2, 3Prime factorization for 9: 3, 3

332 LCM 18

P 192

Practice Problem 2

2, 3 3

92

65 Add

22

92

33

65

184

1815

18

415

1811or

1819

Adding Unlike Fractions

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Step Example

Step 1: Write the prime factorization of each number.

Step 2:

Step 3:

Prime factorization for 5: 5Prime factorization for 9: 3, 3

335 LCM 45

P 192

Practice Problem 3

5 3, 3

94

52 Add

55

94

99

52

4520

4518

45

2018

4538

Adding Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 99Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Step Example

Step 1: Write the prime factorization of each number.

Step 2:

Step 3:

Prime factorization for 4: 2, 2Prime factorization for 5: 5Prime factorization for 10: 2, 5

522 LCM 20

P 192

Practice Problem 4

2, 2 5

109

54

41 Add

22

109

44

54

55

41

2018

2016

205

2018165

20191or

2039

Adding Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 1010Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Subtracting Unlike Fractions

EXAMPLE

SOLUTION

Subtract and simplify:71

43

71

43

44

71

77

43

Step 1: The LCD of 4 and 7 is 28

284

2821

Step 2:

Step 3:284

2821

28

421

2817

Step 4: is in its simplest form. 2817

P 193

Martin-Gay, Basic Mathematics, 4e 1111Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Example

Subtract:

The LCD of the denominators is 33.

10 211 3

10 2 10 211 3 11 3

30 2233 338 33

3 113 11

Simplest form.

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ExampleA freight truck has 1/4 ton of computers, 1/3 ton of televisions, and 3/8 ton of small appliances. Find the total weight of its load.

To find the total weight, add the weights of the individual items.1 1 3Total Weight = 4 3 8

1 1 3= 4 3

6 8 36 8 38

6 8 9= 24 24 24

23= 24

Martin-Gay, Basic Mathematics, 4e 1313Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Step Example

Step 1: Write the prime factorization of each number.

Step 2:

Step 3:

Prime factorization for 12: 2, 2, 3Prime factorization for 24: 2, 2, 2, 3

24 LCM 24, into divides 12 Since

P 193

712 ∙ 2

2 − 524

245

127Subtract

245

2414

24

514

249

Subtracting Unlike Fractions

83

Martin-Gay, Basic Mathematics, 4e 1414Copyright © 2011 Pearson Education, Inc.  Publishing as Prentice Hall.

Step Example

Step 1: Write the prime factorization of each number.

Step 2:

Step 3:

Prime factorization for 10: 2, 5Prime factorization for 7: 7

107 LCM factors,common no have 7 and 10 Since

P 193

Practice Problem 673

109Subtract

1010

73

77

109

7030

7063

70

3063

7033

Subtracting Unlike Fractions

70

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Step Example

Step 1: Write the prime factorization of each number.

Step 2:

Step 3:

Prime factorization for 8: 2, 2, 2Prime factorization for 6: 2, 3

3222 LCM 24

P 194

Practice Problem 7

2, 2, 2 3

65

87Subtract

44

65

33

87

2420

2421

24

2021

241

Subtracting Unlike Fractions

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Solving Problems by Adding or Subtracting Unlike Fractions

EXAMPLE

SOLUTION

The slowest mammal is the three-toed sloth from South America. The sloth has an average

ground speed of mph. In the trees, it can accelerate to mph. How much faster can a sloth travel in the trees? (Source: The Guiness Book of World Records)

101

10017

Step 1: The LCD of 10 and 100 is 100

101

10017

1010

101

10017

10010

10017

Step 2:

Step 3:10010

10017

100

1017

1007

Step 4: mph is in its simplest form. 100

7

P 197

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Solving Problems by Adding or Subtracting Unlike Fractions

Practice Problem 8

SOLUTION

To repair her sidewalk, a homeowner must pour small amounts of cement in three different

locations. She needs of a cubic yard, of a cubic yard, and of a cubic yard for these

locations. Find the total amount of cement the homeowner needs.53

102

Step 1: The LCD of 5, 10 and 15 is 30

152

102

53

22

152

33

102

66

53

304

306

3018

Step 2:

Step 3:30

4618 3028

1514

Step 4: cubic yard is in its simplest form. 1514

P 194

152

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DONE