How important is the Number area in AQA GCSE Mathematics?

Number is the foundation of the whole qualification and is assessed on every paper. It carries a large share of marks at Foundation tier and underpins ratio, algebra and statistics at both tiers. Standard form, fractions and percentages recur constantly, and the non-calculator skills are tested most heavily on Paper 1.

Which Number topics are Higher tier only?

Surds and rationalising the denominator are Higher tier only, as is finding upper and lower bounds and using them in calculations. Fractional and negative indices, recurring decimals to fractions, and harder standard-form calculations are also weighted towards Higher tier, although the core index laws and rounding appear at both tiers.

What Number skills must I be able to do without a calculator?

Paper 1 has no calculator, so you must be fluent with the four operations on integers, decimals and fractions, converting between fractions, decimals and percentages, writing and calculating with standard form, applying the index laws, and rounding and estimating. Drill these mentally and on paper until they are automatic.

What is the most common Number mistake?

The most common errors are sign and place-value slips: getting the power wrong for small numbers in standard form, adding numerators and denominators when adding fractions, and rounding too early in a calculation. Keeping full accuracy until the final answer and checking the size of an answer prevents most of these.

How should I revise the Number area?

Work topic by topic against the specification, mastering place value and the four operations first, then fractions, decimals and percentages, then ratio, indices, rounding and primes. Practise non-calculator methods separately for Paper 1, always show working, and finish with mixed questions that combine several Number skills in one problem.

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AQA GCSE Mathematics Number: a complete overview of place value, fractions, ratio, indices, rounding and primes

A deep-dive AQA GCSE Mathematics guide to the Number area. Covers place value and standard form, fractions, decimals and percentages, ratio and proportion, indices and surds, rounding, estimation and bounds, and factors, multiples and primes, with the non-calculator skills and exam patterns AQA repeats.

Generated by Claude Opus 4.818 min read8300Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What the Number area demands
Place value, standard form and the four operations
Fractions, decimals and percentages
Ratio and proportion
Indices and surds
Rounding, bounds and primes
How the Number area is examined
Check your knowledge

What the Number area demands

Number is the engine room of AQA GCSE Mathematics. Everything else, from algebra to statistics, depends on confident arithmetic, fluent work with fractions, decimals and percentages, and a secure understanding of place value. The examiners test two linked skills: accurate calculation, often without a calculator, and the sensible application of number skills to unfamiliar and multi-step problems.

This guide walks through the six Number topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Place value, standard form and the four operations

The area opens with place value, ordering integers and decimals, and multiplying and dividing by powers of ten. This leads into standard form, writing numbers as $a \times 10^n$ where $1 \le a < 10$ , which is essential for very large and very small numbers and appears on every paper. The four operations on integers and decimals run underneath everything.

Fractions, decimals and percentages

Fractions, decimals and percentages are three ways of writing the same idea, and you must convert freely between them. You need the four operations with fractions, including mixed numbers, and confident percentage work: finding a percentage of an amount, percentage change, and the multiplier method that feeds compound interest in the ratio area.

Ratio and proportion

Ratio and proportion covers simplifying ratios, sharing a quantity in a given ratio, and the unitary method for direct proportion. These ideas link straight into the ratio, proportion and rates of change area and into scale drawings in geometry.

Indices and surds

Indices and surds applies the laws of indices to numbers and algebra, including zero, negative and fractional powers. At Higher tier this extends to surds: simplifying roots, multiplying them and rationalising the denominator so that exact answers can be given.

Rounding, bounds and primes

Rounding and bounds covers rounding to decimal places and significant figures, estimating by rounding to one significant figure, and at Higher tier finding the upper and lower bounds of measurements. Factors, multiples and primes covers prime factorisation and using it to find the highest common factor and lowest common multiple.

How the Number area is examined

A typical AQA profile for Number:

Short calculations. Ordering numbers, converting between fractions, decimals and percentages, writing standard form, and applying index laws.
Multi-step problems. Percentage change, sharing in a ratio, prime factorisation for HCF and LCM, and estimation by rounding.
Reasoning and bounds. Explaining why an estimate is sensible and, at Higher tier, using upper and lower bounds in a calculation.
Non-calculator fluency. Paper 1 tests mental and written arithmetic, fractions and standard form without a calculator.

Check your knowledge

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

Write $0.00056$ in standard form. (1 mark)
Work out $\frac{2}{3} + \frac{1}{6}$ . (2 marks)
Share $£240$ in the ratio $3:5$ . (3 marks)
Evaluate $8^{2/3}$ . (2 marks)
Estimate $\dfrac{59 \times 4.1}{1.9}$ . (2 marks)
Write $90$ as a product of prime factors. (2 marks)
A length is $12$ cm to the nearest centimetre. State its upper and lower bounds. (2 marks)
Increase $£60$ by $15\%$ using a multiplier. (2 marks)

Solutions

Step 1: Write a small number in standard form

Standard form is $a \times 10^n$ where $1 \le a < 10$ . For a small number, the decimal point moves to the right to make the digit in the ones place, so the power of 10 is negative.

$0.00056$ : move the decimal four places right to get $5.6$ , so the power is $-4$ .

5.6 \times 10^{-4}

Final answer: $5.6 \times 10^{-4}$ .

Step 2: Add fractions with different denominators

To add fractions, convert them to a common denominator so the parts are the same size before adding. Add only the numerators, never the denominators.

\frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{5}{6}

Final answer: $\dfrac{5}{6}$ .

Step 3: Share a quantity in a given ratio

Find the value of one share by dividing the total by the sum of the ratio parts. Then multiply by each ratio part to find the two amounts.

Total shares $= 3 + 5 = 8$ . One share $= \frac{240}{8} = 30$ .

3 \times 30 = \pounds 90, \quad 5 \times 30 = \pounds 150

Final answer: $\pounds 90$ and $\pounds 150$ .

Step 4: Evaluate a fractional power

For a fractional power $\frac{m}{n}$ , the denominator is the root and the numerator is the power. Take the root first to keep the numbers small before applying the power.

8^{2/3} = \left(\sqrt[3]{8}\right)^2 = 2^2 = 4

Final answer: 4.

Step 5: Estimate by rounding to one significant figure

Round each number to one significant figure, then carry out the simplified calculation. This gives an answer close to the exact value without requiring a calculator.

\frac{59 \times 4.1}{1.9} \approx \frac{60 \times 4}{2} = \frac{240}{2} = 120

Final answer: 120.

Step 6: Write a number as a product of prime factors

Divide repeatedly by the smallest prime that goes in, building a factor tree until only primes remain. Write the result using index notation where a prime appears more than once.

90 = 2 \times 45 = 2 \times 3 \times 15 = 2 \times 3 \times 3 \times 5 = 2 \times 3^2 \times 5

Final answer: $2 \times 3^2 \times 5$ .

Step 7: State the upper and lower bounds of a rounded measurement

A measurement rounded to the nearest centimetre could be up to half a centimetre above or below the stated value. The lower bound is the smallest value that rounds up to the given measurement; the upper bound is the largest value that rounds down to it.

Lower bound $= 12 - 0.5 = 11.5$ cm; upper bound $= 12 + 0.5 = 12.5$ cm.

Final answer: Lower bound $11.5$ cm, upper bound $12.5$ cm.

Step 8: Increase an amount by a percentage using a multiplier

A percentage increase of $r\%$ corresponds to multiplying by $(1 + r/100)$ , called the multiplier. This combines the original amount and the increase in a single multiplication, which is faster and avoids a two-step method.

Multiplier for a $15\%$ increase is $1.15$ .

60 \times 1.15 = \pounds 69

Final answer: $\pounds 69$ .

Sources & how we know this

AQA GCSE Mathematics (8300) specification — AQA (2015)