The Minus Sign

The minus sign has many meanings and this can lead to confusion and misconceptions.

Thinking of – as opposite will help to overcome some of the difficulties that pupils have with this multi-meaning symbol.

Unary operator

-3 ≡ opposite of 3

-x ≡ opposite of x

-(x + 3) ≡ -x -3 ≡ opposite (x + 3)

-(4 - x) ≡ -4 + x ≡ opposite (4 - x)

-( ) opposite ( )

Binary operator/additive opposite

3 – 2 ≡ 3 + -2

2 – 3 ≡ 2 + -3

3 – x ≡ 3 + -x

x - 3 ≡ x + -3

Multiplicative opposite

Inverse (opposite) function

Reflective opposite

f(-x) ≡ f(x) reflected in y axis

-f(x) ≡ f(x) reflected in x axis

Mixed minus meaning

Changing minus meaning

5 – x = 7 binary

add -5 to both sides

-x = 2 unary