Negative Numbers

Negative Numbers

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

    • $\left(-12\right)÷\left(-4\right)=3$

    • $\left(-6\right)\times \left(-4\right)=24$

  • Two numbers with different signs make a negative

    • $\left(-12\right)÷4=-3$

    • $6\times \left(-4\right)=-24$

• When adding and subtracting with negative numbers

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

    • e.g.  $5-\left(-3\right)=5+3=8$

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

    • e.g.  $7+\left(-3\right)=7-3=4$

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