Negative & Directed Numbers (Cambridge (CIE) IGCSE Maths): Revision Note

Negative & Directed Numbers

What are negative numbers?

• Negative numbers are any number less than zero

  • They may also be referred to as directed numbers

• Negative numbers are indicated by a minus sign (-)

  • To avoid confusion between subtraction and negative numbers, sometimes the following is used:

    • negative numbers are written in brackets

    • a longer dash is used for subtraction (—)

    • the minus for a negative number is raised (superscript), e.g. ^-4

• Negative numbers are read by using the word 'negative' or 'minus' before the value

  • e.g.  -8 would be read/said as "negative eight" or "minus eight"

What are the rules for working with negative numbers?

• When multiplying and dividing with negative numbers

  • Two numbers with the same sign make a positive

    • 

    • 

  • Two numbers with different signs make a negative

    • 

    • 

• When adding and subtracting with negative numbers

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

    • e.g. 

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

    • e.g. 

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