D-27MathsFri 14 Aug

BIDMAS with negatives

Double negatives are the classic 11+ slip.

When a calculation mixes brackets, powers, × ÷ and + −, the order matters. BIDMAS is the UK reminder: Brackets → Indices → Division & Multiplication (left to right) → Addition & Subtraction (left to right). Negatives make the same rules feel trickier — but they still follow BIDMAS.

Picture it: work in layers

× and ÷ share a level — go left to right
+ and − share a level — go left to right
A minus sign stuck to a number (like −3) is part of that number, not a separate “do later” step

Remember — BIDMAS

Brackets — clear the inside first
Indices — powers / square roots (e.g. 3²)
Division and Multiplication — left to right (neither beats the other)
Addition and Subtraction — left to right

Coach tip: rewrite the expression after each step. Messy mental juggling causes most sign errors.

Negatives you’ll meet

Two jobs: (1) double-minus when subtracting, and (2) the four sign rules when you multiply or divide.

Subtracting a negative → plus

3 − (−2) means “3 take away negative 2” → adding 2 → 5

− (−) → +

Sign rules for × and ÷ — all four cases

Same signs → positive answer. Different signs → negative answer. Division follows the same pattern.

(+) × (+) = (+)same → +

4 × 3 = 12

Positive times positive stays positive.

(+) × (−) = (−)different → −

4 × (−3) = −12

Positive times negative is negative.

(−) × (+) = (−)different → −

(−4) × 3 = −12

Negative times positive is negative.

(−) × (−) = (+)same → +

(−4) × (−3) = 12

Negative times negative flips to positive.

Division uses the same sign rules

12 ÷ 3 = 4 (+)÷(+)

12 ÷ (−3) = −4 (+)÷(−)

(−12) ÷ 3 = −4 (−)÷(+)

(−12) ÷ (−3) = 4 (−)÷(−)

Same signs → + · Different signs → −

Exam trap

Two classics: (1) doing + or − before × or ÷; (2) mishandling a squared negative. Lightly — if your child has met indices — −3² usually means −(3²) = −9, while (−3)² means (−3)×(−3) = +9. Brackets change which number is squared.

✓ (−3)²

Square the −3 → (+9)

Watch: −3²

Square 3 first → then the minus → (−9)

Question patterns you might see

Same order-of-ops skill — from plain BIDMAS to negatives and squared signs.

1 · Simple — Multiply before add
5 + 3 × 4 → multiply first: 5 + 12 = 17 (not 32).
2 · Simple — Brackets first
2 × (7 − 3) → brackets: 2 × 4 = 8. Without brackets, 2 × 7 − 3 = 11.
3 · Medium — Left-to-right for × and ÷
24 ÷ 4 × 3 → not “multiply first”. Division and multiplication share priority: left to right → 6 × 3 = 18.
4 · Medium — Subtract a negative
10 − (−6) → subtracting negative six is adding six → 16. Double minus signs are a favourite trap.
5 · Trickier — Negatives with multiply / divide
−5 × 3 + 4 → multiply first: −15 + 4 = −11. The sign travels with the product.
6 · Trickier — Brackets with negatives
8 − (3 − 9) → inside brackets first: 3 − 9 = −6, then 8 − (−6) = 8 + 6 = 14.
7 · Trickiest — Mix of levels + a sign trap
(−2)² − 3 × 4 → indices first: 4 − 3 × 4 → then multiply: 4 − 12 = −8. If someone does (−2)² as −4, or subtracts before multiplying, the answer drifts.

Coach tip: after the answer, ask “Did I honour brackets? Did ×÷ beat +−? Did I keep every minus attached to the right number?” Three yeses usually means you’re safe.

Tomorrow (D-26): inference vs text — what the passage says, and what you can only work out.

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