Fractions

1. Find equivalent fractions and write a fraction in its simplest form

   Multiplying or dividing the top and bottom of a fraction by the same number keeps its value the same - so $\frac{2}{3}$ and $\frac{8}{12}$ are the same amount. To simplify, divide top and bottom by their highest common factor: $\frac{18}{24}$ simplifies to $\frac{3}{4}$ by dividing both by 6.

2. Convert between improper fractions and mixed numbers

   An improper fraction has a top bigger than its bottom, like $\frac{9}{2}$. Divide to convert: 9 ÷ 2 is 4 remainder 1, so $\frac{9}{2}$ = 4 $\frac{1}{2}$. Going the other way, multiply the whole number by the denominator and add the numerator: 3 $\frac{2}{5}$ = $\frac{17}{5}$.

3. Order fractions by writing them with a common denominator

   You can only compare fractions fairly when the bottoms match. To order $\frac{2}{3}$ and $\frac{3}{5}$, rewrite both over 15: $\frac{10}{15}$ and $\frac{9}{15}$ - now it is clear that $\frac{2}{3}$ is bigger. The lowest common multiple of the denominators is the quickest common bottom to use.

4. Add and subtract fractions, including mixed numbers

   Make the denominators match first, then add or subtract the tops only: $\frac{1}{2}$ + $\frac{1}{6}$ becomes $\frac{3}{6}$ + $\frac{1}{6}$ = $\frac{4}{6}$ = $\frac{2}{3}$. With mixed numbers, deal with the whole parts and the fraction parts separately - and if the fractions add past 1, carry into the wholes.

5. Multiply and divide fractions, including mixed numbers

   To multiply, go straight across the tops and bottoms: $\frac{2}{3}$ × $\frac{4}{5}$ = $\frac{8}{15}$ - no common denominator needed. To divide, flip the second fraction and multiply instead: $\frac{3}{4}$ ÷ $\frac{2}{5}$ = $\frac{3}{4}$ × $\frac{5}{2}$ = $\frac{15}{8}$. Convert mixed numbers to improper fractions before you start.

6. Find a fraction of an amount, and write one quantity as a fraction of another

   For a fraction of an amount, divide by the bottom then multiply by the top: $\frac{3}{5}$ of £40 is 40 ÷ 5 × 3 = £24. To write one quantity as a fraction of another, put the first over the second and simplify: 15 minutes out of an hour is $\frac{15}{60}$ = $\frac{1}{4}$.

More Number topics

• Percentages
• Standard Form
• Surds
• Indices
• Bounds & Rounding
• Factors & Multiples

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