Primary Maths Ratios: Count Containers and Contents Separately

Start by naming what the ratio counts

In a public SGExams discussion about PSLE maths, a student helping younger relatives described the difficulty of explaining model solutions. That is a useful starting point for a particular kind of ratio problem: the ratio counts containers, but the question gives a total number of objects inside them. The arithmetic becomes clearer when each number has a label.

This guide uses original examples. They are teaching illustrations, not reproduced examination questions. For curriculum context, Fuhua Primary School’s 2026 upper-primary parent material includes ratio under Primary 6 Standard Mathematics. Follow your child’s actual classroom coverage when choosing practice.

Build one complete group first

Suppose a shop packs small, medium and large bags in the ratio 2:3:5. Each small bag contains one badge, each medium bag contains two badges, and each large bag contains four badges. Ask your child what the numbers 2, 3 and 5 represent. They describe the numbers of bags. They do not yet describe the numbers of badges.

Imagine one complete group containing two small bags, three medium bags and five large bags. There are ten bags in this group. Now count the badges inside those bags.

One complete group therefore contains 10 bags and 28 badges. Both totals describe the same group, but they count different things. Say the units aloud: ten bags, twenty-eight badges. This is the main idea to establish before introducing a larger total.

Use the total that matches the question

If there are 560 badges altogether, the number of complete groups is 560 ÷ 28 = 20. There are ten bags in each group, so the total number of bags is 20 × 10 = 200. The number 20 in the first calculation means complete groups. It does not mean badges per bag or the total number of bags.

A child may instead divide 560 by 10. Ask what ten represents. It is the number of bags in one group, whereas 560 counts badges. Dividing those two numbers does not find the number of complete groups. The table shows why 28 is the matching divisor.

Check the answer by rebuilding the quantities. Twenty groups contain 40 small bags, 60 medium bags and 100 large bags. These hold 40, 120 and 400 badges respectively. The bag counts total 200, and the badge counts total 560. This check uses the original story rather than simply repeating the same division.

Know when the ratio stays the same

If every bag contains the same number of badges, multiplying all three bag counts by that common number preserves the ratio. For example, if every bag held four badges, the badge ratio would be 8:12:20, which simplifies to 2:3:5.

In our original example, the contents per bag are different. The badge ratio is 2:6:20, or 1:3:10. It differs from the bag ratio because the three categories were multiplied by different amounts. This gives your child a reason for the change instead of a rule to memorise without explanation.

Make a short practice session useful

Begin with counters and three drawn bag sizes. Let your child make one complete group, then two groups. Ask them to explain what doubles and what stays the same. Only then replace the counters with the table and a larger total.

For follow-up work, choose a suitable question from the TestPapersFree Primary Maths collection. Before calculating, have your child underline what each ratio counts and label the given total. Finish by asking for one sentence explaining the divisor. A clear explanation of why one group contains a particular number of objects is more useful than completing several similar questions with unlabelled numbers.