Edexcel GCSE Mathematics Number: a complete overview of calculation, fractions, indices, surds, bounds and primes

What the Number content demands

Number is the foundation of Edexcel GCSE Mathematics. Every other area, from algebra and ratio through to geometry and statistics, leans on confident calculation, fluent fraction and percentage work, and a feel for the size of numbers. A large share of these skills sit on Paper 1, where no calculator is allowed, so secure written methods and mental strategies are non-negotiable.

This guide walks through the six areas of the Number content and ties together the matching dot-point pages, each of which has its own practice questions.

Structure and calculation

The number system starts with ordering and place value, using the symbols $<$, $>$, $\le$ and $\ge$. The four operations must be fluent for integers and decimals, including the sign rules for negatives (same signs multiply to a positive, different signs to a negative). The priority of operations, BIDMAS, fixes the order: Brackets, Indices, Division and Multiplication, then Addition and Subtraction. Inverse operations let you check answers and underpin all later rearranging.

Fractions, decimals and percentages

These are three forms of the same idea. Add and subtract fractions with a common denominator; multiply tops and bottoms; divide by multiplying by the reciprocal. Convert freely: divide for fraction to decimal, multiply by $100$ for decimal to percentage. At Higher tier, turn a recurring decimal into a fraction by multiplying by a power of ten and subtracting. Finding a percentage of an amount builds from $10\%$, $1\%$ and $50\%$ blocks on the non-calculator paper.

Standard form and indices

The index laws, $a^m \times a^n = a^{m+n}$, $a^m \div a^n = a^{m-n}$ and $(a^m)^n = a^{mn}$, extend to zero, negative and fractional powers. A negative power is a reciprocal; a fractional power is a root. Standard form writes a number as $A \times 10^n$ with $1 \le A < 10$, making very large and very small numbers manageable, and you calculate with it by handling the number parts and the powers of ten separately.

Surds (Higher)

A surd is a root that stays irrational, like $\sqrt{2}$. Simplify by taking out the largest square factor, $\sqrt{50} = 5\sqrt{2}$; add or subtract only like surds; and rationalise a denominator by multiplying by the surd or its conjugate. Surds keep answers exact, which is why they appear in quadratic, Pythagoras and trigonometry answers.

Rounding, estimation and bounds

Round to decimal places or significant figures using the next digit. Estimate by rounding every value to one significant figure. Bounds give the largest and smallest a rounded value could be, half a unit either side, and at Higher tier you combine bounds in calculations, choosing the extreme that makes the answer biggest or smallest.

Factors, multiples and primes

Every integer is a unique product of primes, found with a factor tree. The HCF takes the lowest powers of shared primes; the LCM takes the highest powers of all primes. Venn diagrams organise the factors, and LCM word problems ask when two repeating events next coincide.

Check your knowledge

A mix of calculation and reasoning questions covering the Number content. Attempt them under timed conditions, then check against the solutions.

1. Work out $-5 + 3 \times (-2)^2$. (2 marks)
2. Work out $\tfrac{3}{4} \div \tfrac{2}{3}$, giving your answer as a mixed number. (2 marks)
3. Write $0.\dot{4}$ as a fraction. (2 marks)
4. Evaluate $8^{\frac{2}{3}}$. (2 marks)
5. Write $0.00056$ in standard form. (1 mark)
6. Simplify $\sqrt{18} + \sqrt{8}$. (2 marks)
7. Write $84$ as a product of its prime factors. (2 marks)
8. Find the LCM of $6$ and $8$. (2 marks)