Progressive Fractions, ratios and proportions practice questions

Use Clevolab for progressive practice in fractions, ratios and proportions. This page shows what the topic covers, what skills the current set targets, and a few real examples from the reviewed question bank.

Maths Progressive Fractions, ratios and proportions

About this topic

Clevolab treats fractions, ratios and proportions as repeated practice with explanation, not just answer checking. This page is designed to make the topic legible before you open the app.

The current Progressive set covers fractions, percentages, ratio, direct proportion, inverse proportion, and proportional reasoning. 227 reviewed questions currently published for this page.

What you can practise

  • Fractions, decimals, and percentages
  • Ratio simplification and sharing
  • Percentage change and reverse percentages
  • Direct and inverse proportion
  • Multi-step proportional reasoning

Real sample questions from the current set

These examples come from the reviewed questions currently stored for this topic. They are here so the page shows the actual flavour of Clevolab, not just a summary.

Level 1

Sample question

Simplify $\tfrac{6}{9}$.

  • A$\tfrac{3}{6}$Answer option
  • B$\tfrac{2}{3}$Correct answer
  • C$\tfrac{3}{2}$Answer option
  • D$\tfrac{6}{3}$Answer option

Why this answer is right

Divide top and bottom by $3$. $\tfrac{6}{9}=\tfrac{2}{3}$.

Find the greatest common factor $3$. $$\tfrac{6}{9}=\tfrac{6\div3}{9\div3}=\tfrac{2}{3}$$ $\tfrac{3}{6}=\tfrac{1}{2}$ and $\tfrac{6}{3}=2$ are different values.

Level 3

Sample question

Simplify the ratio $1.2:0.8:0.4$ to the smallest whole numbers.

  • A$6:4:2$Answer option
  • B$12:8:6$Answer option
  • C$3:2:1$Correct answer
  • D$2:1.5:0.75$Answer option

Why this answer is right

Divide by $0.4$: $1.2\div0.4=3$, $0.8\div0.4=2$, $0.4\div0.4=1$, so $3:2:1$.

To simplify, scale by a factor that clears decimals. Choosing $0.4$ yields integers: $\frac{1.2}{0.4}:\frac{0.8}{0.4}:\frac{0.4}{0.4}=3:2:1$. Longer ratios like $6:4:2$ are equivalent but not simplest.

Level 5

Sample question

Three numbers are in geometric progression. The ratio of the second to the third is $\tfrac{3}{5}$, and the sum of the first two is $15$. Find the first.

  • A$\tfrac{15}{2}$Answer option
  • B$\tfrac{9}{2}$Answer option
  • C$\tfrac{45}{8}$Correct answer
  • D6Answer option

Why this answer is right

Let the GP be $a,ar,ar^2$. With $\tfrac{ar}{ar^2}=\tfrac{1}{r}=\tfrac{3}{5}$, we get $r=\tfrac{5}{3}$. Then $a(1+r)=15$ gives $a=\tfrac{45}{8}$.

In a GP, terms are $a,ar,ar^2$. Given $$\frac{ar}{ar^2}=\frac{1}{r}=\frac{3}{5},$$ so $$r=\frac{5}{3}.$$ Sum of first two is $$a(1+r)=15,$$ hence $$a=\frac{15}{1+5/3}=\frac{15}{8/3}=\frac{45}{8}.$$

How this page fits into Clevolab

Clevolab is broader than any one exam mode. GCSE and A-level pages are useful entry points, while the wider project is about sharpening understanding through repeated topic practice.

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