swiss-algebra-help.com

# Why minus times minus equals plus?

Mike Savage gives a brilliant explanation on the excellent British website of mathtutor. I can't but recommend this website heartily.

So, why "minus times minus equals plus"?

## (-1)x(-1)= 1

We have to remember two arithmetics rules:

1. The rule of precedence (or order of operations, also called BODMAS from Brackets, Orders - squares roots or powers -, Division and Multiplication, Addition and Subtraction)

2. The rule of the distributive law of multiplication (in other words, the multiplication is distributive over addition -> e.g. 3x(5+2)=3x5 + 3x2 )

Then we can now prove that minus x minus = plus.

Let's consider

(-1)x(2+1)

(read "negative one"," times", *two plus one")

Now, for rule 2 (above) the operation can be rewritten as

= (-1)x2 + (-1)x(1)

so, similarly, we can take another operation such as

## (-1)x(-1+1)

and by expanding the brackets (rule 2) we obtain

## =(-1)x(-1) -1

But (-1)x(-1+1) can also be formulated with the rule 1 above (the precedence law, brackets first) as

## = (-1)x(0)

Which simply gives

## =0

Now, we combine the two

## (-1)x(-1) -1 = 0

which is the same to say

and so

## (-1)x(-1) = 1

Q.E.D.

From why minus times minus equals plus back to the study tips webpage

Source, Mike Savage, Mathtutor website

### On the shore of a vast sea

###### Donate

Free 24 hour pass to lynda.com.

Stay in touch with nature. It's full of mathematics!

Enjoy This Site?
Then why not use the button below, to add us to your favorite bookmarking service?

| Homepage| About Us |Study Tips |Contact |

This Website is Powered by Site Build It! - and I would never use anything else.