Fractions, decimals and percentages

Key idea

Fractions, decimals and percentages are three ways of writing the same amount.

$\dfrac{1}{2} = 0.5 = 50\%$ $\dfrac{1}{4} = 0.25 = 25\%$ $\dfrac{3}{4} = 0.75 = 75\%$ $\dfrac{1}{10} = 0.1 = 10\%$ $\dfrac{1}{5} = 0.2 = 20\%$

Converting

• Fraction → decimal: divide the top by the bottom. $\dfrac{3}{8} = 3 \div 8 = 0.375$
• Decimal → percentage: multiply by 100. $0.375 = 37.5\%$
• Percentage → fraction: put it over 100 and simplify. $35\% = \dfrac{35}{100} = \dfrac{7}{20}$

Adding fractions

Make the denominators the same first.

$\dfrac{2}{3} + \dfrac{1}{4} = \dfrac{8}{12} + \dfrac{3}{12} = \dfrac{11}{12}$

Fraction of an amount

Divide by the bottom, multiply by the top.

$\dfrac{3}{5}$ of 40: $40 \div 5 = 8$, then $8 \times 3 = 24$

PERCENTAGE OF AN AMOUNT (no calculator)

Build it from 10% and 5%.

15% of 60: 10% = 6, 5% = 3, so 15% = 9

Common mistake

Adding the tops and the bottoms: $\dfrac{1}{2} + \dfrac{1}{3}$ is NOT $\dfrac{2}{5}$. It is $\dfrac{3}{6} + \dfrac{2}{6} = \dfrac{5}{6}$.