GMAT PREPARATION GUIDE : FRACTIONS

Decimals are one way of expressing the numbers that fall in between the integers. Another way of expressing
these numbers is fractions.

For example 13/2,, the fraction — , which equals 6.5, falls between the integers 6 and 7:

Proper fractions are those that fall between 0 and 1. In proper fractions, the numerator is always
smaller than the denominator. For example:




Improper fractions are those that are greater than 1. In improper fractions, the numerator is greater
than the denominator. For example:


Improper fractions can be rewritten as mixed numbers. A mixed number is an integer and a proper
fraction. For example:

Numerator and Denominator Rules____________
Certain key rules govern the relationship between the numerator (the top number) and the denominator
(the bottom number) of proper fractions. These rules are important to internalize, but keep in mind
that, as written, they only apply to positive fractions.
As the numerator goes up, the fraction increases. If you increase the numerator of a fraction, while
holding the denominator constant, the fraction increases in value:

1 2 3 4 5 6 7 8 9 10
8 8 8 8 8 8 8 8 8 8

As the denominator goes up, the fraction decreases. If you increase the denominator of a fraction,
while holding the numerator constant, the fraction decreases in value as it approaches 0:

3 3 3 3 3 3
2 3 4 5 6 1,000

Adding the same number to both the numerator and the denominator brings the fraction closer to 1,
regardless of the fraction s value.
If the fraction is originally smaller than 1, the fraction increases in value as it approaches 1:

1 1 + 1 2 2 + 9 11 11 + 1,000 1,011 - < -------= - < ------= — < -------------- = --------
2 2 + 1 3 3 + 9 12 12 + 1,000 1,012
1 2 11 1,011
Thus: - < - < — < ------- ...-> 1
2 3 12 1,012
Conversely, if the fraction is originally larger than 1, the fraction decreases in value as it approaches 1:
3 3 + 1 4 4 - > -------= - > -- -+-- 9-= —13 > 13 + 1,000 1,013
2 2 + 1 3 3 + 9 12 12 + 1,000 1,012
-3 > -4> 1—3 > ------- 1,013
2 3 12 1,012
Thus: —13 > --1-,-0-1--3-.. . - » 1