Fractions of a Quantity

In short: To find a fraction of an amount, divide by the bottom number, then multiply by the top number. So $\frac{3}{4}$ of 20 is $20÷4\times 3=15$, because "of" means multiply.

Before you start

• Simplifying fractions to lowest terms.
• Times tables and short division.
• Unit facts: 1 hour $=60$ minutes, 1 kg $=1000$ g, 1 L $=1000$ mL, 1 km $=1000$ m, 1 m $=100$ cm, 1 year $=52$ weeks, a full turn $=360^{\circ }$, a right angle $=90^{\circ }$, a fortnight $=14$ days.

A fraction of an amount

Mixed units: convert first

Change to a smaller unit so the division comes out evenly.

One amount as a fraction of another

Angles as a fraction of a turn

A full turn (a revolution) is $360^{\circ }$. So $270^{\circ }$ is $\frac{270}{360}=\frac{3}{4}$ of a turn, and $18^{\circ }$ is $\frac{18}{360}=\frac{1}{20}$ of a turn.

Quick summary

• To find a fraction of an amount: divide by the denominator, then multiply by the numerator.
• "Of" means multiply.
• Change awkward units to smaller ones first (hours to minutes, kg to g).
• To write one amount as a fraction of another: part over whole, in the same units, then simplify.
• A full turn is $360^{\circ }$, so an angle as a fraction of a turn is $\frac{\text{angle}}{360}$.

Quiz