GCSE Maths grade 4 basics · topic 9 of 9

Non-calculator methods: GCSE Maths grade 4 basics

At least one paper is non-calculator, so you need a reliable written method for each operation. Pick one method you trust and use it every time.

Practise: 12 questions Read the basics first

In plain English

Adding and subtracting: line up the digits by place value (and line up the decimal points) in columns.
Multiplying: the grid method or long multiplication. Split 46 × 23 into 46 × 20 and 46 × 3, then add.
Dividing: short division (the "bus stop"). To divide by a decimal, multiply both numbers by 10 until you are dividing by a whole number.
Decimals: multiply without the points, then count the decimal places in the question and put the same number in the answer. Estimate by rounding each number to 1 significant figure.

Worked example

Work out 34 × 26 without a calculator.

Grid method: 30 × 20 = 600, 30 × 6 = 180, 4 × 20 = 80, 4 × 6 = 24
Add: 600 + 180 + 80 + 24 = 884

Answer: 884

Most common mistake

Wrong0.3 × 0.2 = 0.6

Right0.3 × 0.2 = 0.06

3 × 2 = 6, and there are two decimal places in the question (one in each number), so the answer needs two decimal places: 0.06.

Practice questions (12)

Try each one on paper first, then open the worked answer and mark yourself. You don't need a calculator for any of these.

Q1.Work out 347 + 285
Show worked answer
1. Units: 7 + 5 = 12, write 2 carry 1
2. Tens: 4 + 8 + 1 = 13, write 3 carry 1
3. Hundreds: 3 + 2 + 1 = 6
Answer: 632
Q2.Work out 503 − 178
Show worked answer
1. Units: 3 − 8 won't go, so exchange: 13 − 8 = 5
2. Tens: the 0 became 9 after exchanging from the hundreds; 9 − 7 = 2
3. Hundreds: 4 − 1 = 3
Answer: 325
Q3.Work out 46 × 23
Show worked answer
1. 46 × 20 = 920
2. 46 × 3 = 138
3. 920 + 138 = 1058
Answer: 1058
Q4.Work out 432 ÷ 6
Show worked answer
1. 6 into 4 won't go; 6 into 43 = 7 remainder 1
2. 6 into 12 = 2
3. Answer: 72
Answer: 72
Q5.Work out 3.6 × 4
Show worked answer
1. 36 × 4 = 144
2. One decimal place in the question, so 14.4
Answer: 14.4
Q6.Work out 0.3 × 0.2
Show worked answer
1. 3 × 2 = 6
2. Two decimal places in the question, so 0.06
Answer: 0.06
Q7.Work out 7.2 ÷ 0.3
Show worked answer
1. Multiply both by 10: 72 ÷ 3
2. 72 ÷ 3 = 24
Answer: 24
Q8.Work out 2.4 × 1.5
Show worked answer
1. 24 × 15 = 360 (24 × 10 = 240, 24 × 5 = 120)
2. Two decimal places in the question: 3.60
3. = 3.6
Answer: 3.6
Q9.Work out 12.5 + 7.68
Show worked answer
1. Line up the decimal points: 12.50 + 7.68
2. = 20.18
Answer: 20.18
Q10.Work out 15 − 6.28
Show worked answer
1. Write 15 as 15.00
2. 15.00 − 6.28 = 8.72
Answer: 8.72
Q11.Work out 918 ÷ 17
Show worked answer
1. 17 into 91: 17 × 5 = 85, remainder 6
2. 17 into 68: 17 × 4 = 68
3. Answer: 54
Answer: 54
Q12.Estimate the value of (49.7 × 3.12) ÷ 0.51 by rounding each number to 1 significant figure.
Show worked answer
1. 49.7 ≈ 50, 3.12 ≈ 3, 0.51 ≈ 0.5
2. 50 × 3 = 150
3. 150 ÷ 0.5 = 300
Answer: 300

Can you do these?

Add and subtract whole numbers and decimals in columns
Multiply with the grid method or long multiplication
Divide with short division, including by a decimal
Estimate an answer by rounding to 1 significant figure

Tick them off on the printable checklist. Want more? The Core sections of our free number notes cover the same maths (they are written for IGCSE, but the basics are the same).