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# 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 is0, the number is not a fraction. For example,0/5 = 0. The denominator cannot be0, since dividing by0is 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.

Notethat 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.

Don't work hard; work smart

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fractions.htm**

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## Where are you now?

## Overview of Fractions