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Home > Maths I > Numbers and Money > Basic fractions

Maths I

Basic fractions

Equivalent fractions

A fraction can be written in different ways and still mean the same thing. These are called equivalent fractions.

Look at the shaded areas in this rectangle.

The fractions 3 over 5 and 6 over 10 are represented through coloured blocks within two larger blocks, to show how they are equivalent to each other.

So {3 \over 5} = {6 \over 10}

You can produce lots of equivalent fractions by multiplying or dividing the top and bottom by the same number.

The process of multiplying both numbers in a fraction to create equivalent fractions. 3 over 4 is multiplied by 2 to get 6 over 8, by 3 to get 9 over 12, and by 4 to get 12 over 16. Orange arrows indictate which fraction results from which multiplication.

If you are asked to fill in a missing number, remember that the top and bottom must be multiplied or divided by the same number.

Question

What is the missing number? {4 \over 5} = {? \over 15}

Answer

Here, the bottom is multiplied by 3, so you must multiply the top by 3.

{4 \over 5} = {12 \over 15}

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