Numbers & Arithmetic
Calculators, worked examples and guides — from order of operations and negative numbers through to powers, roots and standard form.
Learning about Numbers & Arithmetic
The key idea: arithmetic fluency is not just about speed — it is about number sense. Understanding how and why operations work builds confidence in every other area of maths. Every advanced topic rests on this foundation.
Type 1 — Order of operations (BODMAS)
"Calculate 3 + 4 × 2 − (6 ÷ 2)"
Step 1: Brackets first: 6 ÷ 2 = 3 → expression becomes 3 + 4 × 2 − 3
Step 2: Multiply: 4 × 2 = 8 → 3 + 8 − 3
Step 3: Left to right: 3 + 8 − 3 = 8
Shortcut: BODMAS — Brackets, Orders, Division/Multiplication, Addition/Subtraction
Type 2 — Negative numbers
"Calculate −4 − (−7)"
Step 1: −(−7) means +7 (double negative = positive)
Step 2: −4 + 7 = 3
Shortcut: "Two negatives make a positive" applies only to multiplication/division — for addition/subtraction, convert the sign then recalculate
Type 3 — Powers and roots
"Calculate 2⁵ and √144"
2⁵ = 2 × 2 × 2 × 2 × 2 = 32
√144: ask "what number squared gives 144?" → 12 × 12 = 144, so √144 = 12
Shortcut: Learn the squares up to 15² = 225 — it saves significant time in exams
Numbers Formula Sheet & Rules
Need a printable revision sheet? Access rules for BODMAS/PEMDAS order of operations, positive and negative integers, index laws, standard form scientific notation, and prime factorisation with step-by-step worked examples and custom print export.
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Numbers & Arithmetic Questions Answered
What is BODMAS?
BODMAS (or PEMDAS in the US) is the order in which mathematical operations must be performed: Brackets, Orders (powers and roots), Division, Multiplication, Addition, Subtraction. Operations of equal priority are worked left to right.
How do negative numbers work?
A negative number is less than zero. Adding a negative is the same as subtracting. Subtracting a negative is the same as adding. So −3 − (−5) = −3 + 5 = 2.
What is a prime number?
A prime number has exactly two factors: 1 and itself. The first primes are 2, 3, 5, 7, 11, 13, 17... Note: 1 is not prime, as it has only one factor.
What is the difference between a square and a square root?
Squaring a number multiplies it by itself (4² = 16). A square root reverses this — it finds the number that was squared to produce the result (√16 = 4).
What is standard form?
Standard form (or scientific notation) writes very large or small numbers as a value between 1 and 10, multiplied by a power of 10. For example: 3,500,000 = 3.5 × 10⁶.