4.6 Fractions and percentages as operators — Learn

Prerequisites: equivalent fractions and multiplication.

Objectives: Interpret fractions and percentages as operators; calculate percentage increases, decreases and original amounts.

Learn the method

An operator acts on an amount. For example, $\frac{3}{5}$ of £20 means multiply £20 by $\frac{3}{5}$. A percentage is a fraction out of $100$. To find a fraction or percentage of an amount, multiply. For a percentage increase, multiply by $1+p/100$. For a decrease, multiply by $1-p/100$.

Worked examples

Example 1. Work out $\frac{3}{8}$ of £56.

Divide £56 by $8$ to find one eighth.

$56\div8=7$.

Multiply by $3$.

$7\times3=£21$.

Example 2. Increase £80 by $15\%$.

The multiplier is $1+15/100=1.15$.

$80\times1.15=£92$.

Example 3. A £72 price is after a $20\%$ reduction. Find the original price.

The new price is $80\%$ of the original.

$72\div0.8=£90$.

Watch out. A $20\%$ reduction does not mean subtracting £20. Find $20\%$ of the price, or multiply by $0.8$. Check that the sale price is below the original.

Progress check

The first shop's discounted price is $£48\times(1-\frac14)=£36$. Compare it with £37.50: $37.50-36=£1.50$, so the first shop costs £1.50 less.

You should now be able to

• find a fraction or percentage of an amount;
• calculate percentage increases and decreases with multipliers;
• find an original amount from a changed amount;
• compare prices after a discount.

Covers: [N11, N12].