Why is a negative times a negative positive?

Multiplying by −1 flips a number to the other side of zero. Doing it twice flips it back, so (−2) × (−3) = +6.

Is −10 bigger than −3?

No. On the number line −10 is further left than −3, so −10 is smaller.

Topic guide · JSS 1, JSS 2

Directed Numbers

Understand negative numbers with a number line. Rules for adding, subtracting, multiplying and dividing directed numbers, with worked examples and practice.

Start the Integers on the Number Line lesson →

Directed Numbers explained

Directed numbers are numbers with a direction: positive numbers are to the right of zero on the number line and negative numbers are to the left. You meet them every day — a temperature of −3 °C, a debt of ₦500, or a floor below the ground floor.

Thinking of a number line makes the rules easy to remember: adding moves you right, subtracting moves you left, and subtracting a negative number is the same as adding.

Key ideas to remember

Adding a positive number moves right on the number line; adding a negative number moves left.
Subtracting a negative is the same as adding: 5 − (−3) = 5 + 3 = 8.
Same signs multiply (or divide) to give a positive answer; different signs give a negative answer.
−7 is less than −2, because it is further to the left on the number line.

Worked example

Evaluate (−2) − (−11).

Step 1: Change − (−) to +
(−2) − (−11) = −2 + 11
Step 2: Answer
= 9

Final answer: 9

Practice questions

Have a go, then open the answer to check your working. Every answer was checked by the MathPlug maths engine.

Question 1
Evaluate (−12) + (−8).
- A4
- B−4
- C20
- D−20
Show answer and working
1. Step 1: Add the negatives
  (−12) + (−8) = −(12 + 8)
2. Step 2: Answer
  = −20
Final answer: −20
Question 2
Evaluate (−11) × (−7).
- A−18
- B−77
- C77
- D−4
Show answer and working
1. Step 1: Signs
  negative × negative = positive
2. Step 2: Answer
  = 77
Final answer: 77
Question 3
Evaluate (−5) × (−3).
- A15
- B−15
- C−8
- D−2
Show answer and working
1. Step 1: Signs
  negative × negative = positive
2. Step 2: Answer
  = 15
Final answer: 15

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Frequently asked questions

Why is a negative times a negative positive?: Multiplying by −1 flips a number to the other side of zero. Doing it twice flips it back, so (−2) × (−3) = +6.
Is −10 bigger than −3?: No. On the number line −10 is further left than −3, so −10 is smaller.