Fractions in Everyday Life

You probably used a fraction today without writing one down. 'Quarter past', 'half price', 'a third of the pizza' and 'the battery is nearly empty' are all fractions. Most real-life fraction problems are the same calculation in disguise: finding a fraction of an amount. Divide by the denominator, then multiply by the numerator. 3/4 of 300 g is 300 ÷ 4 × 3 = 225 g.

Recipes are written for a set number of people, so changing the number of servings means multiplying by a fraction. A cake for 8 people that uses 300 g of flour needs 6/8 = 3/4 of the amounts for 6 people: 3/4 × 300 = 225 g. For 12 people you need 12/8 = 3/2, or 1 1/2 times as much: 450 g. If a recipe asks for 3/4 of a cup of milk and you are making half the amount, you need 1/2 × 3/4 = 3/8 of a cup.

An hour has 60 minutes, so a quarter of an hour is 60 ÷ 4 = 15 minutes, half an hour is 30 minutes, and three quarters of an hour is 45 minutes. A third of an hour is 20 minutes, which is why '20 minutes' and '1/3 of an hour' mean the same thing.

Many currencies split one unit into 100 smaller units, such as cents. A quarter of 1 euro or 1 dollar is 25 cents and a fifth is 20 cents. A sale sign saying '1/3 off' a jacket priced EUR 45 means you save 45 ÷ 3 = EUR 15 and pay EUR 30. Note that paying 2/3 of the price is the same thing seen the other way round.

When things do not split into whole numbers, fractions give the fair answer. Three pizzas shared equally between four friends gives each person 3 ÷ 4 = 3/4 of a pizza. This is the idea that a fraction is a division: 3/4 means 3 ÷ 4. You could cut each pizza into quarters and give everyone one quarter from each pizza, so each friend still gets 3 quarters.

Metric units are based on 10, 100 and 1,000, which makes fractions of them easy to work out. Half a litre is 1,000 ÷ 2 = 500 ml. Three quarters of a kilogram is 750 g. A quarter of a metre is 25 cm, and a fifth of a kilometre is 200 m. Building, sewing and science all use these conversions.

A football match under the Laws of the Game is played in two equal halves of 45 minutes, so each half is 45/90 = 1/2 of the normal playing time (any added time is extra). Statistics such as success rates are fractions too: a basketball player who scores 18 of 24 free throws has a success rate of 18/24, which simplifies to 3/4, or 75%.

Probability is written as a fraction. A fair coin lands heads with probability 1/2, and the chance of rolling a 6 on a fair six-sided dice is 1/6. Gauges show fractions as well: many fuel gauges are marked E, 1/4, 1/2, 3/4 and F, and a phone showing 25% has about a quarter of its charge left.