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).
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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.
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.
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).
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.
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.
Classic trap: a price is £360 after a 20% discount. The original is 360 ÷ 0.80 = £450, not 360 + 20%.
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.
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 ✓)
Standard form writes numbers as a × 10ⁿ with 1 ≤ a < 10 and n an integer. The power counts how far the decimal point moves.
Not standard form: 15 × 10⁷ — because 15 > 10. Rewrite as 1.5 × 10⁸.
Tap an ordinary number, then its matching standard form.
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.
Key facts: a⁰ = 1 (not 0); a negative index means reciprocal, so 2⁻³ = 1/8 — it is not negative.
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.
Extended tip: for the largest area multiply the upper bounds; for the smallest, the lower bounds.
A rational number can be written as a fraction; an irrational one cannot. Tap a number, then its box.
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.
You've worked through Number for Cambridge IGCSE Mathematics (0580). 🎉
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