A ** fraction** is a number of the form ±

*a*/

*b*, where

*a*and

*b*are positive integers. The number

*a*is called the

**and**

*numerator**b*is called the

**. The numerator tells you the number of equal parts, and the denominator tells you how many of those parts make up a whole. Often fractions are numbers that fall between integers. Fractions are also used to show division.**

*denominator*Some examples:

3/5 of the cake means 3 pieces of a cake which is divided into 5 equal pieces.

The fraction 7/4 is a number between 1 and 2.

6*x*/2 = 6*x* ÷ 2 = 3*x*

If a fraction’s numerator and denominator are equal (e.g. 5/5), the fraction is equal to 1.

(All 5 pieces of a cake that is cut into 5 pieces is 1 whole cake.)

A fraction that has zero as its numerator (e.g. 0/5) is equal to zero. (Zero pieces of the cake that is cut into 5 pieces.)

A fraction that has zero as its denominator (e.g. 8/0) is *undefined*.

Note: On the GMAT, fractions may be shown in either of two formats. You will need to understand both.

Fractions can be on one line, like 3/5 = (*x* + 2)/10.

They can also be “built up,” like:

\\[1ex]\dfrac{3}{5} = \dfrac{\textit{x}+2}{10}

**Fractions and Decimals**