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Maths Lab · Free lesson · 18 minutes

A ratio compares parts; a fraction names a whole

Distinguish part-to-part and part-to-whole comparisons, share a total in a ratio and connect the result to a percentage.

JSS2 · ratio and conversion

01 · Think first

Start with a question.

A fruit drink uses two cups of concentrate for three cups of water. Concentrate:water is 2:3, but concentrate is not two thirds of the finished drink.

What you already know
  • Count equal units
  • Simplify fractions
  • Convert a simple decimal into a percentage
For red:blue = 2:3, what fraction of all counters are red?

02 · See it

Keep track of the whole

A ratio unit has the same size in both parts. Scaling the recipe changes each amount by the same factor.

Concentrate units
2
Water units
3
Total units
5
Concentrate fraction
2/5 = 0.4 = 40%

Use the justified worked steps below to explore this idea.

03 · Show steps · explain why

One justified step at a time.

  1. 1

    Concentrate:water = 2:3; total units = 2 + 3 = 5

    A colon compares the two parts. Adding the parts identifies the whole.

04 · Mistake clinic

Find the first wrong idea.

Tempting wrong line

Boys:girls = 3:5, so boys are 3/5 of the class.

Compare the correction and its reason

Boys are 3/(3 + 5) = 3/8 of the class.

Five counts only the girls' ratio units. The class includes both parts, so there are eight units in the whole.

Check: The two fractions of the whole should add to one: 3/8 + 5/8 = 1.

A mistake is evidence about the next idea to repair. It is not a label for the learner.

05 · Your turn

Try first. Then use a hint.

1. Share 600 in the ratio 1:2. Enter the smaller share.guided practice
2. Boys:girls = 3:5. What percentage of the whole class are boys? Enter the percent number.independent practice
3. A recipe uses flour:sugar = 5:2. If sugar is 120 g, how many grams of flour are needed?far practice

06 · Check & reflect → next step

Understanding includes explaining.

Say what each side of your comparison measures. Is the denominator another part, or the whole?

Choose your next learning need

Use ratios and equations together to model costs or mixtures. If percentage bases are still unclear, revisit the percentage lesson.

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Source and review status

JEM-J2-M03-001 · Phase 3B JSS2 Mathematics REPAIRED · Lesson 2 · printed pp. 11–12

This published free lesson contains selected explanations and authored practice. Complete canonical volumes and tutor solutions remain in the protected Content Vault.