# Overview of Fractions

by Ron Kurtus (revised 18 February 2009)

A fraction is a part of the whole. It is a form of number that indicates the quotient or division of two whole numbers, except 0.

The top number of a fraction is called the numerator and the bottom number is the denominator. An improper fraction is one where the numerator is larger than the denominator. A mixed number is a whole number plus a proper fraction. An improper fraction should be reduced to a mixed number.

Questions you may have include:

• What is a description of a fraction?
• What are examples of mixed numbers?
• How do you reduce an improper fraction?

This lesson will answer those questions.

## Fraction definition

A fraction indicates a part of the whole or the quotient of two whole numbers, except 0.

Note: If the numerator is 0, the number is not a fraction. For example, 0/5 = 0. The denominator cannot be 0, since dividing by 0 is forbidden.

### Fraction is part of the whole

If you would take a pie and divide it into five equal pieces, then one piece would be one-fifth (1/5) of the whole pie. In this way, a fraction indicates it is part of the whole. Two pieces of this pie would be 2/5 of the whole pie.

Since a fraction is part of the whole, a proper positive fraction is always less than 1.

### Incomplete division

Typically, you divide a number by a smaller number, such as 6 ÷ 2 = 3. If you try to divide a number by a larger number, the result is called a fraction. It is incomplete division. For example, 2 ÷ 3 = 2/3, which is a fraction.

Note that the the ÷ sign almost looks like a fraction, with the dots representing numbers. Also, the / sign is often used as division instead of the ÷ sign.

### Numerator and denominator

The top number in a fraction is called the numerator. The bottom number is called the denominator. I don't know of any easy way to remember that, but since the words are used so much when dealing with fractions, it is worthwhile to learn them.

### Can't use 0 in a fraction

If the numerator in a quotient is 0, then the number cannot be a fraction, since 0 divided by any number is 0. For example 0/5 = 0.

On the other hand, you cannot have a denominator equal to 0. You cannot have 3/0, because that is 3 ÷ 0, and you cannot divide by 0. That is a basic rule in arithmetic.

## Mixed numbers

A mixed number is a whole number plus a fraction. 5 2/3 is a mixed number. It is called "five and two-thirds" and is the same as the sum of 5 + 2/3.

Other examples of mixed numbers include 1 1/2, 3200 7/10 and 15 23/24.

## Reducing an improper fraction

An improper fraction is a fraction where the numerator is larger than the denominator. For example, 7/5 is an improve fraction, since 7 is greater than 5.

An improper fraction can be reduced to a mixed number, consisting of a whole number and a fraction. This is done by dividing numerator by the denominator. The remainder of the division is the numerator of the new fraction.

Consider the improper fraction 37/5. If you divide 37 by 5, you will get an answer of 7 and a remainder of 2. Thus your mixed number is 7 2/5.

### Examples

Since most improper fractions do not entail large numbers, you can usually perform the division in your head, as opposed to using long division.

Consider 5/4. 5 divided by 4 equals 1 with a remainder of 1.

5/4 = 1 1/4

32/3 is 32 divided by 3 equals 10 with a remainder of 2.

32/3 = 10 2/3

126 divided by 25 equals 5 with a remainder of 1.

126/25 = 5 1/25

### No remainder

If there is no remainder, the improper fraction simply becomes a whole number:

27/9 = 3

64/4 = 16

## Summary

A fraction indicates a part of the whole or the quotient of two whole numbers except 0. The top number of a fraction is called the numerator and the bottom number is the denominator. An improper fraction is one where the numerator is larger than the denominator. A mixed number is a whole number plus a proper fraction. An improper fraction should be reduced to a mixed number.

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