Fractions: Introduction

Do you know what a fraction is? Do you know what the two numbers in a fraction are called? Do you know how to convert a fraction to a decimal number or how to expand/reduce a fraction? That's what this article is about.

The number above the line is called numerator and it says how many equal parts there are. The number below the line is called denominator and it says how many of these parts make up a whole. The line itself is called fraction bar .

This is an illustration of the fraction . The numerator is 3, because there are three equal parts, and the denominator is 4, because that is the number of parts that make up the whole pizza.

How to read a fraction?

If the numbers are too big, we use the word OVER:

Conversion to decimal numbers

We can easily convert fractions to decimal numbers. How? We simply divide the numerator (the number above the fraction bar) by the denominator (the number below the fraction bar).

Proper and improper fractions

If the numerator is less than the denominator, the value of the fraction is less than 1 and the fraction is called proper fraction .

If the numerator is greater than the denominator, the value of the fraction is greater than 1 and the fraction is called improper fraction .

If the numerator is equal to the denominator, the value is 1. Such fractions are also IMPROPER.

Why are they called IMPROPER? Well, because a FRACTION should be something that's broken down into pieces, a piece of something. Let's have a look at a picture of another pizza:

This is what the fraction would look like. The pieces do not fit together. It is actually one whole pizza and a fraction (a quarter) of another pizza:

And that is what a mixed number is.

Mixed numbers

A mixed number is a combination of a whole number and a fraction:

An improper fraction can be converted to a mixed number.

Let's take 5/2 for example.

First, we divide the numerator by the denominator. Five divided by two is 2 with the remainder 1.

The number 2 will be the whole number and the remainder will be the numerator. The denominator will be equal to the denominator in the original fraction.

We can convert a mixed number to an improper fraction in the following way:

Let's take the result of the conversion above:

First, we multiply the whole number by the denominator: 2 x 2 = 4

Now we add the numerator: 4 + 1 = 5

The number 5 will be the numerator of the improper fraction, the denominator will not change.

Equivalent fractions

If we multiply the numerator and the denominator of a fraction by the same number, the value will stay the same.

This process is called expansion (we expand a fraction) .

If we divide the numerator and the denominator of a fraction by the same number, the value will, once again, stay the same.

This process is called reduction or simplification (we reduce or simplify a fraction) .

The value of the following four fractions is the same:

We call them equivalent fractions.

How is this possible? Have a look at the following two pictures:

You can see that (three quarters of a pizza) is actually the same as (six eighths of a pizza).

NOW YOU...

• know what a fraction is
• understand the terms numerator, denominator and fraction bar
• understand the difference between a proper fraction, improper fraction and a mixed number
• can convert a fraction to a decimal number
• can convert an improper fraction to a mixed number and vice versa
• know what equivalent fractions are
• can expand and reduce fractions