Chapter 2: Review

Resolve the chapter problem

To make identical packs from 24 blue and 36 red counters, the number of packs must be a common factor of 24 and 36.

The HCF is $2^2\times3=12$. The greatest possible number is 12 packs, each with 2 blue counters and 3 red counters.

Mixed practice

Work without looking back. For each question, choose a method and give a reason for your choice.

1. List all factors of 30. Is 31 prime? Explain your answer.
2. Find the prime factorisation of 84. Use it to find the HCF and LCM of 36 and 84.
3. A badge uses one of three shapes and one of four colours. List the outcomes in a table, then count them. Which method makes completeness easiest to check?
4. A two-digit code uses digits 1 to 5 without repetition. How many codes are possible? Explain why the product rule applies.
5. Recall from Chapter 1: work out $18-25$ and estimate $398\times21$ by rounding each number first.
6. Recall from Chapter 1: round 6.284 to two decimal places. Explain which digit decides the rounding.

Reflect

Which method can you now use with more confidence: factor pairs, prime factorisation, an organised list, or the product rule? Write one question you could solve with it, and name a check for your answer.