# Maths: ratio basics

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## Reducing ratios to their simplest form

To reduce a ratio to its simplest form divide it by its highest common factor.

Put into practise: Write the ratio 15:18 in its simplest form.

Their highest common factor is 3 so, divide them both by 3 = 5 : 6

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## If the ratio contains decimals or fractions multip

Multiply both sides to get rid of the decimal or fraction and then divide both sides by the highest common factor.

Put into practise: simplify the ratio 2.4 : 3.6 as far as possible.

Times both sides by 10 = 24 : 36 now divide by 12 = 2:3

If you have a fraction as a ratio make both of the fractions have the same common denominator and then multiply both sides by the common denominator number once done, the fraction is gone and there is only a ratio divide by the highest common factor if there are any

Put into practise:
5/4 : 7/2 to get the Same denominator times the second fraction by two and then times 4 by 4 and this leads to 5:14.

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## If the ratio has mixed units convert to the smalle

Put into practice: Reduce the ratio 24mm : 7.2cm to its simplest form.
1) convert 7.2cm into mm 24mm:72mm
2) now to cancel down, divide by the HCF which is 12 = 1:3

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## To get to the form 1:n or n:1 - just divide

Put into practise: Reduce 3:56 to the form 1:n

Divide both sides by 3
1:18 2/3

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