Negative Numbers (Edexcel IGCSE Maths)

Spec point — 1.4A

Negative numbers

What are the rules for calculations with negative numbers?

• When multiplying and dividing with negative numbers

  • Two numbers with the same sign make a positive

    • (−12)÷(−4)=3
    • (−6)×(−4)=24

  • Two numbers with different signs make a negative

    • (−12)÷4=−3
    • 6×(−4)=−24

• When adding and subtracting with negative numbers

  • Subtracting a negative number is the same as adding the positive

    • e.g. 5−(−3)=5+3=8

  • Adding a negative number is the same as subtracting the positive

    • e.g. 7+(−3)=7−3=4

Where are negative numbers used in real-life?

• Temperature is a common context for negative numbers

  • If the temperature is 3°C, and it cools by 5°C, the new temperature will be -2°C

    • This is equivalent to 3 - 5 = - 2

  • If the temperature is -4°C, and it warms up by 6°C, the new temperature will be 2°C

    • This is equivalent to (-4) + 6 = 2

  • To explain why (-5) - (-6) = 1, you could think of it as follows:

    • A room is -5°C, then -6°C of cold air is 'removed'
    • The room now warms to 1°C

• Money and debt is another common context for negative numbers

  • A negative sign means you owe money

  • If someone has a debt of £200, and they borrow another £400, their total debt is now £600

    • This is equivalent to (-200) + (-400) = -600

  • If someone is in debt by £300, but then pays off £200 of their debt, they are now only £100 in debt

    • This is equivalent to (-300) + 200 = -100

Exam Hint Your calculator isn't always as clever as you may think!

Using brackets around negative numbers will always make sure the calculator is doing what you want.

e.g. The square of negative three is (−3)×(−3)=9. On many calculators, $-3^{2}=-9$ but (−3)²=9. The second one is correct.

Worked Example Complete the following table.

Calculation	Answer
3 + (-4)
(-5) + (-8)
7 - (-10)
(-8) - (-6)
(-3) × 6
(-9) × (-2)
(-9) ÷ (-3)
(-10) ÷ 5

Answer :

Calculation	Working	Answer
3 + (-4)	3 - 4	Final answer: -1
(-5) + (-8)	(-5) - 8	Final answer: -13
7 - (-10)	7 + 10	Final answer: 17
(-8) - (-6)	(-8) + 6	Final answer: -2
(-3) × 6	3 × 6 = 18 one is negative	Final answer: -18
(-9) × (-2)	9 × 2 = 18 both are negative	Final answer: 18
(-9) ÷ (-3)	9 ÷ 3 = 3 both are negative	Final answer: 3
(-10) ÷ 5	10 ÷ 5 = 2 one is negative	Final answer: -2