## Fraction Basics

A **fraction** is a part of a whole. The top part of a fraction is called the **numerator**. The bottom part of a fraction is called the **denominator**. The denominator of a fraction is the number of equal parts into which the whole has been divided, while the numerator is the number of those equal parts in the fraction. So, for example, the fraction ¾ means that a whole has been broken up into four equal parts, and this fraction represents three of them.

When a fraction is written in words, the numerator is written as a counting number (that is, one, two, three, four, and so on) and the denominator is written as an ordinal number (third, fourth, fifth, etc.). The only exception is when the denominator is two, in which case we use *half* or *halves*. It is usually correct put a hyphen in between the numerator and denominator when you write a fraction in words, although it is not necessary to do this when writing common expressions like “a half” or “a third,” and it is not recommended when the denominator is higher than twenty, as the use of multiple hyphens can be confusing. Here are some examples:

- ⅔: two-thirds
- 1/7: one-seventh
- 11/23: eleven twenty-thirds
- 1/75: one seventy-fifth

Fractions may be either proper or improper. In a **proper fraction**, the numerator is smaller than the denominator. Some examples of proper fractions are ½, ⅗, and 9/10. In an **improper fraction**, on the other hand, the numerator is larger than the denominator. Some examples of improper fractions are 2/1, 4/3, and 12/5. A **mixed number** includes both a whole number and a fraction. A few examples of mixed numbers are 1 ½, 5 ¼, and 12 ⅓.

A fraction is said to be in its **simplest form** when the numerator and denominator do not have any common factors other than 1. In other words, if the numerator and denominator can each be evenly divided by a number besides 1, the fraction is not yet in its simplest form. To reduce a fraction to its simplest form, divide the numerator and denominator by their greatest common factor. For example, in the fraction 12/20, both numerator and denominator are evenly divisible by 4, so the fraction can be reduced to ⅗.

You may be asked to compare the size of fractions with unlike denominators. The easiest way to do this is to divide the numerator by the denominator and compare the resulting decimals. For example, imagine you are asked to compare ¾ and ⅝. ¾ = 3 ÷ 4 = 0.75 and ⅝ = 5 ÷ 8 = 0.625, so ¾ > ⅝.