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Equivalent Fract ions

GMAT

Equivalent fractions can be created by multiplying/dividing the numerator and denominator by thsame number.

1

2

1

2

3

3

3

6

Examples:

5

3

7

3

7

15

5

5

3

Multiply by 3 Multiply by 3

1 3

2 6

Multiply by 5 Multiply by 5

3 15

7 35

Practice: Fill in the blank

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

1

2 12

Answers:

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

6

6

61

2 12

2

3 24

8

8

62

3 24

1

4 16

9

4

4

6

9 6

4

3

1

3

5 60

12

1

63

5 02 6

3

1 7

4

7

7

7

4 2

1

8

5

6 42

7

7

55

6 42

3

7 49

8

7

7

9

8 6

7

5

4

2

9 108

12

12

22

9 108

4

7

15 135

9

9

7

15 135

63

1

5 245

49

49

41

5 245

9

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Simpl ifying Fractions

To simplify a fraction, divide the numerator and denominator by the samenumber until the numerator and denominator can be simplified no further.

8

40

56

40

5 86

5

7

Examples:

Divide by 8 Divide by 8

42

54

42

54

21

27

21

2

2

3

27 3

7

9

Divide by 2 Divide by 2

Can be simplified further

Divide by 3 Divide by 3

Cannot be simplified further

Practice: Simplify each fraction

a)

b)

c)

d)

e)

f)

g)

h)

i)

Answers:

a)

b)

c)

d)

e)

f)

g)

h)

i)

Cannot be

simplified further

15

20

15

20

5 3

45

18

27

18

27

9 2

39

40

48

40

48

8 5

68

7

13

7

13(already simplified

60

150

60

150

30

3

2

50

39

52

39

52

13

1

3

43

135

215

135

215

7

43

5

5

2

121

154

121

154

11

11

11

14

72

108

72

108

36

3

2

36

2

5

numerator

denominator

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Converting Fractions

Convert ing an entire f raction to a mixed fr action:

1) Determine how many times the denominator divides into the numerator (this becomesthe whole number)

2) The remainder becomes the numerator of the new fraction

3) The denominator remains the same

Entire fractions

7

2

20

3

40

17

Mixed fractions

13

2

26

3

62

17

Lets look at converting entire fractions to mixed fractions and converting mixed fractionsto entire fractions

Examples: 7

2 23

1 The denominator (2) divides into the numerator (7) three

times, with a remainder ofone

32

5 56 2 The denominator (5) divides into the numerator (32) six times,

with a remainder oftwo

51

4 4

21

32

7 7

23

Converting a m ixed fraction t o an entire fr action:

1) Multiply the whole number by the denominator and add the product to the numerator

2) The result becomes the new numerator and the denominator remains the same

Examples: The whole number (5) multiplied by the denominator (4)equals 21. The denominator (4) remains the same

The whole number (3) multiplied by the denominator (7)equals 22. The denominator (7) remains the same

Practice questionson the next page

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a)

b)

c)

d)

e)

f)

Practice: Convert each entire fraction to a mixed fraction Answers:

a)

b)

c)

d)

e)

f)

9

4

19

5

35

2

40

7

68

11

59

6

12

4

43

5

117

2

55

7

2

6 11

59

6

a)

b)

c)

d)

e)

f)

Practice: Convert each mixed fraction to an entire fraction Answers:

a)

b)

c)

d)

e)

f)

13

4

13

4

38

5

42

9

111

15

93

20

130

3

43

5

22

9

26

15

69

20

91

3

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Adding and subt racting fr act ions

(1) Create equivalent fractions with the same denominator (a.k.a. common denominator)

(2) Add/subtract the numerators, and keep the denominator the same

Examples: 3 1

4 6

3 1

4 6

9

3

2

12

2

3 2

12

11

12

Create equivalent fractions with the same denominator (12)

Add the numerators; keep the denominator the same

8 5

9 12

8 5

9 12

32 15

36

4

36

3

4

17

36

3

Create equivalent fractions with the same denominator (36)

Subtract the numerators; keep the denominator the same

a)

b)

c)

d)

e)

f)

Practice: Answers:

a)

b)

c)

d)

e)

f)

3 1

8 12

14 7

15 10

7 3

16 8

1 2

8 3

1 51

2 6

5 9

6 10

11

24

7

30

1

16

19

24

2

3

26

15

111

15or

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Multiplying fr actions

Multiply numerator by numerator, and denominator by denominator.

9 4 36 3 16 3

16 15 240 24

2

120 20

Method 1:

9 4 9 4 4 3 1 3

16 15 16 1

3

5 4 5 204 3Cross simplify:

Cross sim plif ying

Whenever possible, cross simplify beforehand.

2 5 10

11 7 77

5 1 5

6 7 42

Examples:

a)

b)

c)

d)

e)

f)

Practice: Find each product and write answer in simplest terms Answers:

a)

b)

c)

d)

e)

f)

3 7

5 9

21 16

32 35

7 9

24 14

8 3

15 4

11 4

16 33

72 25

125 96

7

15

3

10

3

16

2

5

1

12

3

20

2

5

numerator

denominator

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Fractions Refres

Dividing fractions

Multiply by the reciprocal of the divisor.

Examples:

4 11

9 20

4 20

9 11

80

99

flip to become and multiply11

20

20

11

3 5

7 8

3 8

7 5

24

35

flip to become and multiply5

8

8

5

a)

b)

c)

d)

e)

f)

Practice: Find each quotient and write answer in simplest terms Answers:

a)

b)

c)

d)

e)

f)

8

21

9 15

16 16

21 14

40 25

8 1

15 20

27 11

32 8

2 3

7 4

5 1

6 5

25

6

14

6or

3

5

15

16

32

3

210

3or

3

4

GMAT