Directed numbers with brackets (challenge)

2026-10-19Numbers & Estimation Ms Lam

Mixed operations with multiple brackets — the step that trips many S2–S3 students in timed papers.

Key formulas

\text{Work innermost brackets first}

Then \times and \div \text{left to right}

Then + and - \text{left to right}

Order of operations with signs

Keep BODMAS/BIDMAS, but treat every directed number as a signed packet. Rewrite a−(−b) as a+b before combining. Never drop a minus when removing brackets after a minus sign.

Multiple brackets

Evaluate the innermost pair first. When a minus sits before a bracket, multiply every term inside by −1. Example pattern: 5−[3−(−2)] = 5−[3+2] = 5−5 = 0.

Word contexts

Time-zone and temperature questions use directed numbers. If Hong Kong is 0 and Region A is −5 hours, a clock reading must shift carefully — draw a quick timeline rather than guessing the sign.

Exam habit

Rewrite the entire expression after every bracket removal so one slip does not cascade.

Worked example

Nested brackets

Problem. Evaluate (−6) − [4 − (−9)].

Solution. Inner: 4 − (−9) = 13. Then (−6) − 13 = −19.

Review quiz

1 / 4

(−6)−[4−(−9)] =

Practice questions

Evaluate (−6) − [4 − (−9)].
Evaluate 2 × (−5 + 3) − (−8).
Evaluate −3[2 − (5 − 9)].
Hong Kong is 0 h. City B is −7 h. If it is 21:00 in Hong Kong, what is the time in City B?

Study notes

Do I multiply before adding inside brackets?

Inside a bracket, still follow normal order. The bracket only forces that whole result to be used next.

Why do I lose marks on signs?

Usually from distributing a minus incorrectly — write every step.