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Fractions in Action

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Fractions in Action

Solve each problem and show working where asked. Give fraction answers in simplest form. Use dollars and cents where appropriate.

Fraction toolkit

Start with equivalent fractions and operations, then put them to work in everyday situations.

1.A. Simplify 84/126 fully. Show one common factor you divide by.

2.B. Put these fractions in order from least to greatest: 5/8, 2/3, 7/12. Use the number line to help you compare them.

3.C. Work out 5/6 − 3/10. Give your answer in simplest form.

4.D. A hiking group has 18 L of water. They use 2/3 of it before lunch, then 1/4 of the original amount after lunch. How many litres remain?

Fractions in the real world

Use careful reasoning: in each situation, check what the fraction is a fraction of.

5.E. A jacket costs $240 and is reduced by 3/10 of its original price. What is the sale price?

6.F. A recipe for 8 people uses 3/4 kg of kūmara. How much kūmara is needed for 12 people, assuming the recipe scales directly?

7.G. A tank is 5/6 full. After 14 L is drained, it is 1/2 full. What is the tank’s total capacity?

8.H. Choose the correct result for (3/5) ÷ (9/10).

2/3
3/2
27/50
1/6

9.I. True or false? For any non-zero number n, n × 7/9 is always greater than n. Explain your decision.

10.J. A fundraiser sells 160 tickets. 3/8 are bought online, and 5/16 are bought at the door. The rest are sold in advance. What fraction of the tickets are sold in advance, and how many tickets is that?