Directed numbers: add, subtract, multiply and divide

2026-10-01Numbers & Estimation Mr Chan

Use number-line sense and sign rules so directed-number calculations stay accurate under exam pressure.

Key formulas

(+a)+(+b)=+(a+b)

(-a)+(-b)=-(a+b)

(+a) \times (-b)=-(a \times b)

(-a) \times (-b)=+(a \times b)

What directed numbers mean

A directed number carries both size and direction. Positive values sit to the right of zero on the number line; negative values sit to the left. Temperature below zero, bank overdrafts and positions relative to sea level are everyday directed-number contexts for Secondary 2.

Addition and subtraction

Adding a positive number moves right; adding a negative number moves left. Subtraction means add the opposite: a − b = a + (−b). When the signs match, keep the common sign and add the absolute values. When the signs differ, subtract the absolute values and keep the sign of the larger absolute value.

Multiplication and division

Same signs give a positive product or quotient; different signs give a negative result. Work absolute values first, then attach the correct sign. Never leave a double sign such as 5 + (−3) unmarked — rewrite it as 5 − 3 before calculating.

Exam habit

Circle every sign change. For a chain of operations, compute one step at a time and rewrite the expression after each step so a slip does not cascade.

Worked example

Directed-number chain

Problem. Evaluate (−8) + 5 − (−3) × 2.

Solution. Multiplication first: (−3) × 2 = −6. Expression becomes (−8) + 5 − (−6). Then (−8) + 5 = −3, and −3 − (−6) = −3 + 6 = 3.

Review quiz

1 / 4

What is (−9) + (−4)?

Practice questions

Evaluate (−7) + (−5) and (−7) − (−5).
Find (−12) × 4 and (−12) ÷ (−3).
Simplify 8 + (−15) − (−6).
Explain why (−3) × (−5) is positive.

Study notes

Is subtracting a negative the same as adding?

Yes. a − (−b) = a + b.

What if absolute values are equal?

Their sum is zero; their difference is zero only when the numbers are identical.