Before I start this topic, let me demonstrate a shortcut in maths. I can show a multiplication by using the “×” symbol. For example, 8 × 2 = 16. But another way, which is especially useful when dealing with negative numbers is to use brackets with no “×” symbols: (8)(2) = 16, that is (8)(2) means 8 × 2.

So, if two positive numbers are multiplied or divided by one another, you already know that the result is positive.

(8)(2) = 16 (Remember the “+” symbol is assumed to be there for positive numbers)

8 ÷ 2 = 4

Now if the signs of the numbers are different, the result of the arithmetic is negative:

(-8)(2) = (8)(-2) = -16

(8) ÷ (-2) = (-8) ÷ (2) = -4

The reason for this is because multiplication is really just successive adding. For example, (-8)(2) is a shortcut for adding (-8) twice, That is (-8)(2) means (-8) + (-8) which is -16.

Now if both numbers are negative, the result is positive. It’s that double negative effect again. So

(-8)(-2) = 16

(-8) ÷ (-2) = 4

These rules are easy to remember: Like signs are positive, unlike signs are negative.

Tomorrow, let’s talk about fractions and more maths shortcuts.