Background reading · Mathematics and Statistics

Percentages in the wild: sales, GST and tricky deals

How percentages work in shops, why 35% off is the same as paying 65%, and the percentage tricks worth watching for.

Per cent means 'out of 100'. 25% is 25 out of 100, which is the same as the fraction 1/4 and the decimal 0.25. Percentages are everywhere money is: sales, taxes, interest rates and phone data. Since 10 July 1967, when New Zealand switched from pounds, shillings and pence to decimal currency, all our money has worked in hundredths too: 100 cents in a dollar.

Finding a percentage

Use 10% as a building block. To find 10%, divide by 10: 10% of $180 is $18. Then 5% is half of that ($9), 30% is three lots ($54), and 35% is 30% + 5% = $63. With a calculator, change the percentage to a decimal and multiply: 0.35 × $180 = $63.

Subtract the discount: 35% off $180 is $180 − $63 = $117.

Multiply by what you still pay: if 35% comes off, you pay 65%, so 0.65 × $180 = $117.

GST

Most prices you see in New Zealand shops already include GST, a 15% tax on goods and services. If a builder quotes '$400 plus GST', the real price is $400 × 1.15 = $460. That little 'plus GST' is worth $60.

Tricky deals

Up and down: a price goes up 50%, then comes down 50%. $100 becomes $150, then $75. It doesn't get back to where it started, because the second 50% is of a bigger number.

'Buy two, get one free': only a deal if you wanted three. If you did, it is like paying for 2 out of 3, about 33% off.

'Was' prices: a sale is only a sale if the item really sold at the 'was' price. New Zealand's Fair Trading Act says businesses must not mislead you about prices.

The habit that beats every trick: estimate first, then calculate. If a '40% off' price is more than half the original, something is wrong.

Sources and further reading

Written for Kōkiri Learn students in our own words. Check facts against the sources.

Used in: Money Moves: Budgets, Percentages and Interest