GCSE Maths · Edexcel 1MA1 · Foundation & Higher · Grades 1–5 · Number

Non-Calculator Methods

Paper 1 of the Edexcel GCSE is non-calculator, a third of your marks. These written methods for decimals, long multiplication and division, fractions, percentages and estimation are worth practising until they are automatic.

1Place value: multiplying and dividing by 10, 100, 1000

Multiplying by 10 moves every digit one place to the left, so the number gets bigger. Dividing moves digits to the right. Use as many places as there are zeros.

Calculation	Answer
3.6 × 100	360
0.072 × 1000	72
45 ÷ 1000	0.045
8.1 ÷ 10	0.81

Avoid

Saying “add a zero” when multiplying by 10. It fails for decimals: 3.6 × 10 is 36, not 3.60.

2Adding and subtracting decimals

Line up the decimal points in a column. Fill empty places with zeros so every number has the same number of decimal places.

Worked example

Work out 20 − 7.36.

Write 20 as 20.00.
Subtract in columns, borrowing as needed: 20.00 − 7.36.

12.64

3Long multiplication

Use either the column method or the grid method. The grid method is slower but easier to check.

Worked example

Work out 347 × 26 using the grid method.

Split each number into place values:

×	300	40	7
20	6000	800	140
6	1800	240	42

First row: 6000 + 800 + 140 = 6940.
Second row: 1800 + 240 + 42 = 2082.
Total: 6940 + 2082 = 9022.

347 × 26 = 9022

Exam tipEstimate first: 347 × 26 ≈ 350 × 25 = 8750. Your answer should be close to this. If you get 90 220 or 902, you’ve misplaced a digit.

4Multiplying decimals

Ignore the decimal points and multiply the whole numbers.
Count the total number of decimal places in the question.
Put that many decimal places in the answer.

Worked example

Work out 4.7 × 3.2.

47 × 32 = 1504.
4.7 has 1 decimal place and 3.2 has 1, so the answer has 2.

15.04

Worked example

Work out 2.3 × 0.4.

23 × 4 = 92.
There are 2 decimal places in total, so 92 → 0.92.

0.92

5Short and long division

Worked example

Work out 864 ÷ 6 using short division (the “bus stop” method).

6 into 8 goes 1, remainder 2. Carry the 2 to make 26.
6 into 26 goes 4, remainder 2. Carry the 2 to make 24.
6 into 24 goes 4.

144

Worked example

Work out 3768 ÷ 24 using long division.

24 into 37 goes 1 (24), remainder 13. Bring down 6 → 136.
24 into 136 goes 5 (120), remainder 16. Bring down 8 → 168.
24 into 168 goes 7 exactly.

157

Dividing by a decimalTo divide by a decimal, multiply both numbers by 10, 100, … until the divisor is a whole number. The answer doesn’t change.
4.8 ÷ 0.2 = 48 ÷ 2 = 24 · 2.56 ÷ 0.08 = 256 ÷ 8 = 32

6Fractions without a calculator

Operation	Method	Example
Add / subtract	Common denominator first	23 + 14 = 812 + 312 = 1112
Multiply	Change mixed numbers to improper fractions, then multiply tops and bottoms	2½ × 1⅓ = 52 × 43 = 206 = 3⅓
Divide	Keep, change, flip: multiply by the reciprocal	34 ÷ 25 = 34 × 52 = 158 = 178

Exam tipAlways simplify and give mixed numbers in the form the question asks for. “Show that” questions need every step written down.

7Percentages without a calculator

Build any percentage from 10%, 5% and 1%:

Worked example

Find 35% of 240.

10% = 24, so 30% = 72.
5% = 12.
35% = 72 + 12.

Worked example

Find 17.5% of 60.

10% = 6, 5% = 3, 2.5% = 1.5.
17.5% = 6 + 3 + 1.5.

10.5

8Estimating answers

Round every number to 1 significant figure, then calculate. Write down your rounded values, because they earn the method mark.

Worked example

Estimate the value of 49.8 × 3.10.48.

Round: 50 × 3 ÷ 0.5.
50 × 3 = 150, and 150 ÷ 0.5 = 300.

≈ 300

Over or under?Rounding the numerator up or the denominator down makes the estimate too big (an overestimate).

Common mistakes

Misplacing the decimal point when multiplying decimals. Count the decimal places in the question.
Not lining up decimal points when adding or subtracting.
Adding fractions by adding the denominators: 12 + 13 is not 25.
Forgetting to convert mixed numbers before multiplying or dividing.
Rounding to 1 decimal place instead of 1 significant figure when estimating.

★Key Vocabulary Recap

Place value: The value of a digit depends on its position.
Significant figure: The first non-zero digit and those after it.
Reciprocal: 1 ÷ the number; for a fraction, flip it.
Estimate: An approximate answer from rounded values.
Improper fraction: A fraction whose numerator is bigger than its denominator, e.g. 74.

Specification reference (Pearson Edexcel GCSE (9–1) Mathematics 1MA1: N2, N3, N8, N12, N14)

N2: apply the four operations, including formal written methods, to integers, decimals and simple fractions.
N3: use conventional notation for the priority of operations; use inverse operations.
N8: calculate exactly with fractions.
N12: interpret fractions and percentages as operators.
N14: estimate answers; check calculations using approximation.

Next stepReady to practise? Try the 14 exam-style questions, then check your working against the worked solutions.

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GCSE Maths · Edexcel 1MA1 · Foundation & Higher · Grades 1–5 · Number