Mammoth Memory

Multiplying and dividing Negatives

In mathematics there are rules for multiplying and dividing positive and negative numbers.

The rules are:

1 - When the signs are different the answer is negative
2 - When the signs are the same the answer is positive 

Or another way of remembering this is:

My friend's friend is my friend (positive x positive = positive)
My friend's enemy is my enemy (positive x negative = negative)
My enemy's friend is my enemy (negative x positive = negative)
My enemy's enemy is my friend (negative x negative = positive)

The main issue to remember is:

A negative x negative is a positive – 2 wrongs make a right!

My enemy’s enemy is my friend

Examples

`3times5` `=` `15`   (signs are the same so positive)
`-3times5` `=` `-15`   (signs are different so negative)
`3times-5` `=` `-15`   (signs are different so negative)
`-3times-5` `=` `15`   (signs are the same so positive)

  

`6-:2` `=` `3`   (signs are the same so positive)
`-6-:2` `=` `-3`   (signs are different so negative)
`6-:-2` `=` `-3`   (signs are different so negative)
`-6-:-2` `=` `3`   (signs are the same so positive)

 

 

NOTE:

If there were three negatives in a row:

`-3times-5times-5`

Then you would complete one calculation first

`-3times-5=15`

And now relook at the equation

`15times-5`

You now complete this calculation

`15times-5=-75`

So `-3times-5times-5=-75`

How can a negative x negative be a positive?

The following may help explain why:

Your mum says:

      Running total of cash available  
You got paid     `£100`   `£100`
Next you got paid    `£100`   `£200`
The following day you were paid       `£100`   `£300`
Then an electric bill came in for     `-£50`   `£250`
Then another electric bill came in for   `-£50`   `£200`
And the next day another electric bill came for    `-£50`   `£150`

 

Then the electricity company wrote to you to say
they had made a terrible mistake and they shouldn’t
have sent the bills. So they need to take back the
bills as follows:

Subtract `-3` lots of `-£50`   `£150`   `£300`

 

Summary

`-3` lots of `-£50` is `+£150`

Because `-3times-£50=£150`

Two negatives make a positive.

There is another way of looking at this as follows:

Look at the following sequence:

`2times5` `=` `10`
`1times5` `=` `5`
`0times5` `=` `0`
`-1times5` `=` `-5`
`-2times5` `=` `-10`
`-3times5` `=` `-15`

 

Notice that the number on the left drops by one each time and the total on the right drops by 5 each time.

Now do the same but with a -5

`2times-5` `=` `-10`
`1times-5` `=` `-5`
`0times-5` `=` `0`
`-1times-5` `=` `5`
`-2times-5` `=` `10`
`-3times-5` `=` `15`

 

Notice that the number on the left drops by one each time and the total on the right climbs by 5 each time.

Two negatives have to make a positive.

 

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