GCSE Maths grade 4 basics · topic 1 of 9

Number skills: GCSE Maths grade 4 basics

Order of operations, negative numbers, rounding, factors and primes. These small skills turn up inside almost every other question, so they are worth getting fast and accurate.

Practise: 11 questions Read the basics first

In plain English

BIDMAS tells you the order: Brackets, Indices (powers and roots), then Division and Multiplication, then Addition and Subtraction.
Negative numbers: subtracting a negative is the same as adding. Two signs the same give a positive answer when you multiply or divide; two different signs give a negative.
Rounding: look at the next digit along. 5 or more rounds up; 4 or less stays the same.
Factors divide into a number exactly; multiples are in its times table; a prime has exactly two factors, 1 and itself.

Worked example

Work out 20 − 12 ÷ 4 + 2 × 3

Division and multiplication first: 12 ÷ 4 = 3 and 2 × 3 = 6
Now 20 − 3 + 6, working left to right
20 − 3 = 17, then 17 + 6 = 23

Answer: 23

Most common mistake

Wrong5 + 3 × 4 = 8 × 4 = 32

Right5 + 3 × 4 = 5 + 12 = 17

Working left to right ignores BIDMAS. Multiplication comes before addition, so do 3 × 4 first.

Practice questions (11)

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 5 + 3 × 4
Show worked answer
1. Multiply first: 3 × 4 = 12
2. Then add: 5 + 12 = 17
Answer: 17
Q2.Work out (8 − 2) × 3 − 4²
Show worked answer
1. Brackets: 8 − 2 = 6
2. Indices: 4² = 16
3. Multiply: 6 × 3 = 18
4. Subtract: 18 − 16 = 2
Answer: 2
Q3.Work out −7 + 12
Show worked answer
1. Start at −7 on a number line and move 12 to the right
2. You pass 0 after 7 steps, then 5 more steps
Answer: 5
Q4.Work out −4 × −6
Show worked answer
1. 4 × 6 = 24
2. Two negative signs: the answer is positive
Answer: 24
Q5.The temperature at midnight is −3 °C. At noon it is 8 °C. By how many degrees has it risen?
Show worked answer
1. Rise = 8 − (−3)
2. Subtracting a negative is adding: 8 + 3 = 11
Answer: 11 °C
Q6.Round 3.476 to 1 decimal place.
Show worked answer
1. Keep one digit after the point: 3.4|76
2. The next digit is 7, which is 5 or more, so round up
Answer: 3.5
Q7.Round 48 627 to the nearest thousand.
Show worked answer
1. The thousands digit is 8: 48|627
2. The next digit is 6, so round up to 49 000
Answer: 49 000
Q8.Round 0.0582 to 1 significant figure.
Show worked answer
1. The first significant figure is the first non-zero digit: 5
2. The next digit is 8, so the 5 rounds up to 6
3. Keep the zeros in front: 0.06
Answer: 0.06
Q9.List all the factors of 18.
Show worked answer
1. Find factor pairs: 1 × 18, 2 × 9, 3 × 6
2. 4 and 5 do not divide 18 exactly, and after 3 × 6 the pairs repeat
Answer: 1, 2, 3, 6, 9, 18
Q10.Write 60 as a product of its prime factors.
Show worked answer
1. 60 = 2 × 30
2. 30 = 2 × 15
3. 15 = 3 × 5
4. So 60 = 2 × 2 × 3 × 5
Answer: 2² × 3 × 5
Q11.Work out √81 + 2³
Show worked answer
1. √81 = 9, because 9 × 9 = 81
2. 2³ = 2 × 2 × 2 = 8
3. 9 + 8 = 17
Answer: 17

Can you do these?

Use BIDMAS in a calculation
Add, subtract, multiply and divide negative numbers
Round to decimal places, significant figures and the nearest 10, 100 or 1000
Find factors, multiples and primes, and write a number as a product of primes

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).