Maths283 views·Updated 29 Jul 2026·2 pages

Understanding Fractions: Adding, Multiplying, Dividing, and Converting

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Fraction operations might seem tricky at first, but they're actually...

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Mastering Fraction Operations

Adding fractions is all about finding a common denominator first. Look at the example: $\frac{1}{5} + \frac{3}{4}$ becomes $\frac{4}{20} + \frac{15}{20} = \frac{19}{20}$ when you convert both fractions to twentieths.

The process is simple: find the lowest common multiple of your denominators, convert both fractions, then add the numerators together. Keep the denominator the same throughout—only the top numbers get added!

Multiplying fractions is actually easier than adding them. Simply multiply the numerators together, multiply the denominators together, then simplify if possible. For example: $\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10}$ .

Dividing fractions uses the "keep, change, flip" method. Keep the first fraction as it is, change the division sign to multiplication, then flip the second fraction upside down. So $\frac{1}{6} \div \frac{1}{5}$ becomes $\frac{1}{6} \times \frac{5}{1} = \frac{5}{6}$ .

Quick tip: Remember that dividing by a fraction is the same as multiplying by its reciprocal—this trick will save you loads of time in exams!

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Essential Fraction, Decimal, and Percentage Conversions

These key equivalences are absolute must-knows for your GCSE—memorise them now and thank yourself later! Half is 0.5 or 50%, a quarter is 0.25 or 25%, and a fifth is 0.2 or 20%.

Some trickier ones to remember: $\frac{1}{3}$ equals 0.333... or 33.3%, whilst $\frac{2}{3}$ is 0.666... or 66.6%. An eighth ( $\frac{1}{8}$ ) converts to 0.125 or 12.5%.

Ordering fractions and decimals becomes much easier when you convert everything to the same form—usually percentages work best. In the example, $\frac{1}{4}$ becomes 25%, 0.4 becomes 40%, $\frac{3}{4}$ becomes 75%, and 0.3 becomes 30%.

This means the correct order from smallest to largest would be: $\frac{1}{4}$ (25%), 0.3 (30%), 0.4 (40%), $\frac{3}{4}$ (75%).

Exam strategy: Converting everything to percentages makes comparing much quicker than working with mixed fractions and decimals!

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Maths283 views·Updated 29 Jul 2026·2 pages

Understanding Fractions: Adding, Multiplying, Dividing, and Converting

mollie@mollie_cte63dcfbxdbw

Add to Google sources

Fraction operations might seem tricky at first, but they're actually quite straightforward once you know the basic rules. This guide covers the three main operations—adding, multiplying, and dividing fractions—plus essential fraction-to-decimal conversions you'll need for GCSE maths.

of 2

Mastering Fraction Operations

Quick tip: Remember that dividing by a fraction is the same as multiplying by its reciprocal—this trick will save you loads of time in exams!

of 2

Essential Fraction, Decimal, and Percentage Conversions

These key equivalences are absolute must-knows for your GCSE—memorise them now and thank yourself later! Half is 0.5 or 50%, a quarter is 0.25 or 25%, and a fifth is 0.2 or 20%.

Some trickier ones to remember: $\frac{1}{3}$ equals 0.333... or 33.3%, whilst $\frac{2}{3}$ is 0.666... or 66.6%. An eighth ( $\frac{1}{8}$ ) converts to 0.125 or 12.5%.

This means the correct order from smallest to largest would be: $\frac{1}{4}$ (25%), 0.3 (30%), 0.4 (40%), $\frac{3}{4}$ (75%).

Exam strategy: Converting everything to percentages makes comparing much quicker than working with mixed fractions and decimals!

We thought you’d never ask...

You can download the app from Google Play Store and Apple App Store.

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Samantha KlichAndroid user

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Mastering Fraction Operations

Essential Fraction, Decimal, and Percentage Conversions

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