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Arithmetic : Fractions

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Multiplication and Division of Fractions

 

To multiply fractions, multiply the numerators to get the numerator of the product, and multiply the denominators to get the denominator of the product.

 

Example
A jug contains 20 ounces of orange juice. If Janet consumes two-fifths of the juice in the jug, then how many ounces of orange juice did she drink?
Solution. A whole number may be written as a fraction with 1 as its denominator, e.g., 20 = 20/1.

20

1
× 2

5
= 40

5
= 8.

 

Thus, Janet drank 8 ounces of orange juice.

When multiplying fractions, it is very convenient to cancel a common factor by dividing the numerator and denominator by the factor.
Remember do not multiply your problems. Dividing simplifies your problems.
For example to multiply 15/8 by 44/21, divide 15 and 21 by the common factor 3, and divide 8 and 44 by the common factor 4 as shown below.

15

8
× 44

21
= 15 × 44

8 × 21
= 5 × 11

2 × 7
= 55

14
.

Time and effort are saved in the above example by not multiplying 15 by 44, and 8 by 21.
Note that canceling can be done only between a numerator and a denominator of the same fraction or another fraction, but not between two numerators or between two denominators.


 

Division of fractions involves reciprocals. A fraction is the reciprocal of another fraction if their product is 1.
The reciprocal of a fraction is obtained by inverting the fraction, i.e., by interchanging the numerator and denominator.
So, the reciprocal of a fraction n/m is m/n, where both n and m are non-zero.
For example, the reciprocal of 2/5 is 5/2 and the reciprocal of 1/5 is 5.

To divide a fraction (dividend) by another fraction (divisor), multiply the dividend by the reciprocal of the divisor.
For example,

8

9
÷ 3

5
= 8

9
× 5

3
= 40

27
.

 

Example
Debbie stitches a doll's dress in three-fourths of an hour. If Debbie works for 5¼ hours, then how many dresses will she stitch?
Solution. The first step is to convert the mixed number to a fraction. Now, 5¼ = 21/4, since 5  × 4 + 1 = 21.
In 3/4 hour, one dress is stitched.
So in 21/4 hours, 21/4 ÷ 3/4 dresses are stitched.

21

4
÷ 3

4
= 21

4
× 4

3
= 21

3
= 7.

Thus, Debbie will stitch 7 dresses in 5¼ hours.

 

GMAT Math Review - Arithmetic : Index for Fractions
 

GMAT Math Review - Arithmetic : Practice Exercise for Fractions

 

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10 more pages in GMAT Math Review

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