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Number, proportion and ratio

Build fluency with fractions, percentages, standard form, proportion and ratio in practical settings.

12 free questions · Notes · Worked solutions

Practise this topic

What you will practise

  • Convert between fractions, decimals and percentages.
  • Use ratio to divide quantities and compare rates.
  • Apply percentage change and direct proportion.
  • Calculate with standard form and sensible rounding.

Revision notes

Fractions and percentages

A fraction is a division: a/b. To find p% of a quantity Q, calculate (p/100)Q. A percentage multiplier is 1+p/100 for an increase and 1-p/100 for a decrease. Reverse percentages require dividing by the multiplier.

Ratio and rates

A:b has a+b total parts. Divide a total by the sum of the parts, then multiply by each part. A rate compares unlike units, such as distance per time; convert units before comparing.

Proportion and standard form

For direct proportion y=kx, the ratio y/x stays constant. Standard form is A×10^n with 1≤A<10. Keep units attached and round only at the end unless instructed otherwise.

Common checks

A percentage decrease cannot make a positive amount larger. In a:b, swapping the order changes which quantity each part represents. Estimate first to catch misplaced decimal points.

A worked example

A school club has 84 members. The ratio of musicians to actors is 3:4. Then 25% of the musicians join a new project. How many musicians join it?

  1. The ratio has 3+4=7 equal parts.
  2. One part is 84÷7=12 members.
  3. There are 3×12=36 musicians.
  4. 25% is one quarter, so 36÷4=9.

9 musicians

Try it yourself

These are original practice questions, not official past-paper questions. Practice points count correct final answers; working is not automatically assessed.

Choose a question to begin.
Question 1 · Standard1 practice point

Write 0.375 as a fraction in simplest form.

Need a hint?

Write the decimal over 1000, then simplify.

Worked solution
  1. 0.375=375/1000.
  2. Divide numerator and denominator by 125 to get 3/8.
Question 2 · Standard1 practice point

A jacket costs £80 and is reduced by 15%. What is its sale price?

Need a hint?

Find 85% of £80.

Worked solution
  1. The remaining fraction is 1−0.15=0.85.
  2. 80×0.85=68.
Question 3 · Standard1 practice point

Share 56 in the ratio 3:5. What is the larger share?

Need a hint?

There are eight parts in total.

Worked solution
  1. One part is 56÷8=7.
  2. The larger share is 5×7=35.
Question 4 · Standard1 practice point

Which is the correct standard form of 0.000072?

Need a hint?

Move the decimal point until the leading number is between 1 and 10.

Worked solution
  1. 0.000072 becomes 7.2 after moving 5 places right.
  2. Moving right gives a negative power: 7.2×10^-5.
Question 5 · Foundation1 practice point

Find 18% of 250.

Need a hint?

Calculate 0.18×250.

Worked solution
  1. 18%=0.18.
  2. 0.18×250=45.
Question 6 · Standard2 practice points

A map uses the scale 1:25 000. Two villages are 7.2 cm apart on the map. Find their actual distance in kilometres.

Need a hint?

Multiply the map length by 25 000, then convert centimetres to kilometres.

Worked solution
  1. Actual distance=7.2×25 000=180 000 cm.
  2. 100 000 cm=1 km, so the distance is 1.8 km.
Question 7 · Standard2 practice points

A phone bill rises from £48 to £54. Find the percentage increase.

Need a hint?

Divide the increase by the original amount.

Worked solution
  1. Increase=54−48=6.
  2. 6÷48×100=12.5%.
Question 8 · Standard2 practice points

A drink is made by mixing concentrate and water in the ratio 2:7. How many millilitres of concentrate are needed for 630 ml of finished drink?

Need a hint?

Count all nine parts before finding the two concentrate parts.

Worked solution
  1. There are 2+7=9 parts.
  2. One part is 630÷9=70 ml.
  3. Concentrate is 2×70=140 ml.
Question 9 · Stretch2 practice points

A £120 item is discounted by 20%, then the discounted price is increased by 10%. Find the final price in pounds.

Need a hint?

Apply the two multipliers in sequence.

Worked solution
  1. After discount: 120×0.80=96.
  2. After increase: 96×1.10=105.60.
Question 10 · Foundation2 practice points

A car travels 156 km in 2.4 hours. Find its average speed in km/h.

Need a hint?

Average speed equals distance divided by time.

Worked solution
  1. Speed=156÷2.4.
  2. 156÷2.4=65 km/h.
Question 11 · Standard2 practice points

A recipe for 6 people uses 450 g of flour. How much flour is needed for 10 people? Give your answer in grams.

Need a hint?

Find the amount per person, then scale to ten.

Worked solution
  1. 450÷6=75 g per person.
  2. 75×10=750 g.
Question 12 · Stretch2 practice points

Calculate (3.6×10^5)÷(1.2×10^2). Give the answer in ordinary form.

Need a hint?

Divide the coefficients and subtract the powers.

Worked solution
  1. 3.6÷1.2=3.
  2. 10^5÷10^2=10^3.
  3. 3×10^3=3000.

Coverage and sources

Selected IGCSE concepts, with a mix of introductory and more demanding questions. Check your own specification. AI drafted; independent teacher review is pending. Editorial details.

Cambridge IGCSE Mathematics 0580 syllabus

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