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Cambridge IGCSE Maths (0580) · Number
Mini-Lesson

Number

This mini-lesson covers Number for Cambridge IGCSE Mathematics (0580): types of number, HCF & LCM, fractions, decimals & percentages, ratio & proportion, standard form, indices, surds and bounds (Extended content included).

Honest heads-up: the quick-fire games here test your recall of facts, formulae and methods — not full written working. In the real exam you must show every step.

Work through each screen, answer the questions and collect ⭐ stars. Press Start.

Types of number

Types of number, HCF & LCM

Know your number families: natural (1, 2, 3…), integers (…−2, −1, 0, 1…), primes (2, 3, 5, 7…), squares, cubes and rational vs irrational. Every integer is a unique product of primes.

72 = 2³ × 3²keep dividing by primes until only primes remain

For the HCF take the lowest power of each shared prime; for the LCM take the highest power of every prime that appears.

Remember: HCF ≤ each number ≤ LCM. The HCF is the small answer (shared factors only); the LCM is the big one.

Calculate

Your turn

136 = 2² × 3² and 48 = 2⁴ × 3. Work out the highest common factor (HCF) of 36 and 48.
Hint: lowest power of each shared prime = 2² × 3 = 4 × 3.
Calculate

Your turn

2Find the lowest common multiple (LCM) of 8 and 12.
Hint: 8 = 2³, 12 = 2²×3, so LCM = 2³ × 3 = 8 × 3.
Fractions

Fractions of an amount

To add or subtract, use a common denominator. To find a fraction of a quantity, divide by the denominator then multiply by the numerator. To divide by a fraction, multiply by its reciprocal (flip the second one).

Worked example

Work out ⅜ of £64.

64 ÷ 8 = 8, then 8 × 3 = £24

Divide ≠ flip both: ¾ ÷ ⅔ = ¾ × 3/2 = 9/8, only the second fraction flips.

Calculate

Your turn

3Work out ⅖ of 350.
Hint: 350 ÷ 5 = 70, then × 2.
Percentages

Percentages & reverse percentages

Use a multiplier: increase by 12% → ×1.12; decrease by 12% → ×0.88. For compound change, raise the multiplier to a power. For a reverse percentage (given the final amount, find the original), divide by the multiplier.

amount = P × (multiplier)ⁿreverse: original = final ÷ multiplier

Classic trap: a price is £360 after a 20% discount. The original is 360 ÷ 0.80 = £450, not 360 + 20%.

Calculate

Your turn

4A television costs $480. In a sale its price is reduced by 15%. Work out the sale price.
$
Hint: multiplier for −15% is 0.85, so 480 × 0.85.
Calculate

Your turn

5$3000 is invested at 4% per year compound interest. Work out the value after 2 years.
$
Hint: 3000 × 1.04² = 3000 × 1.0816.
Quick check

Quick check

?A jacket costs £90 after a 25% reduction. What was the original price?
Ratio & proportion

Ratio & direct proportion

To share in a ratio, add the parts to find the total number of parts, then find one part. For direct proportion use the unitary method: find the value of one, then scale.

Worked example

Share $200 in the ratio 3 : 2. Total = 5 parts, one part = 200 ÷ 5 = $40.

Shares: 3×40 = $120 and 2×40 = $80 (check 120+80 = 200 ✓)

Calculate

Your turn

6$450 is shared between Ann and Bo in the ratio 4 : 5. How much does Bo receive?
$
Hint: 9 parts total, one part = 450 ÷ 9 = 50, Bo has 5 parts.
Standard form

Standard form

Standard form writes numbers as a × 10ⁿ with 1 ≤ a < 10 and n an integer. The power counts how far the decimal point moves.

150 000 000 = 1.5 × 10⁸small numbers use negative powers, e.g. 0.0004 = 4 × 10⁻⁴

Not standard form: 15 × 10⁷ — because 15 > 10. Rewrite as 1.5 × 10⁸.

Quick check

Quick check

?Which number is written correctly in standard form?
Match game

Ordinary ⇄ standard form

Tap an ordinary number, then its matching standard form.

Indices & surds

Indices & surds

Index laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ. Also a⁰ = 1, a⁻ⁿ = 1/aⁿ, a^(1/n) = ⁿ√a. A surd is a root that isn't a whole number; simplify by pulling out square factors.

√50 = √25 × √2 = 5√28^(2/3) = (³√8)² = 2² = 4

Key facts: a⁰ = 1 (not 0); a negative index means reciprocal, so 2⁻³ = 1/8 — it is not negative.

Calculate

Your turn

7Work out the exact value of 3⁻². Give your answer as a fraction's decimal value.
Hint: 3⁻² = 1 ÷ 3² = 1 ÷ 9 = 0.111…
Calculate

Your turn

8Simplify √72 to the form k√2. Type the value of k.
Hint: √72 = √36 × √2, and √36 = 6.
Bounds

Upper & lower bounds

A rounded value hides a range. A length of 8 cm to the nearest cm lies from 7.5 up to (but not including) 8.5.

bounds = value ± ½ × (rounding unit)lower = 8 − 0.5 = 7.5 · upper = 8 + 0.5 = 8.5

Extended tip: for the largest area multiply the upper bounds; for the smallest, the lower bounds.

Calculate

Your turn

9A mass is 6.0 kg to the nearest 0.1 kg. Write down the upper bound.
kg
Hint: half of 0.1 is 0.05, add it to 6.0.
Sort it

Rational or irrational?

A rational number can be written as a fraction; an irrational one cannot. Tap a number, then its box.

➗ Rational

√ Irrational

Recap

Key points

Types & factors: primes, squares, cubes; HCF = lowest shared powers, LCM = highest powers.

Fractions & %: fraction of an amount; multipliers; compound = ×(mult)ⁿ; reverse % = ÷ multiplier.

Ratio: share by parts; unitary method for proportion.

Standard form: a × 10ⁿ with 1 ≤ a < 10.

Indices & surds: a⁰ = 1, a⁻ⁿ = 1/aⁿ; simplify surds by square factors.

Bounds: value ± ½ × rounding unit.

You've covered the Number essentials for Cambridge IGCSE Maths (0580). Press Finish to see your score.

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