Negative numbers

I thought I'd post this as I have seen a lot of my students struggle with this

OK….We all know what numbers are: 1, 2, 3, 4……etc.
Did you know that numbers can also be negative? You must have heard of temperatures of being minus ten degrees before (especially if you're into snowboarding!). Minus ten as a number is written as -10. Any number with - before it can also be called a negative number.
We can have as many negative numbers as we have normal (positive or plus) numbers - the only funny number sitting on the fence is zero, which is always called zero - not negative zero or positive zero.

The numbers can be seen in a range like the one below:
………….-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6………..

Negative numbers surprisingly appear quite a lot in everyday life. If you owe your parents £8 and have no other money it could be said that you have £ -8. Similarly, it is very important for all businesses to know how much money they don't have or they could go bust.
We've already mentioned temperatures being negative, but how about the speed of a car - how can you travel at -20 miles per hour? - By going backwards of course!

Negatives of anything are opposites for the positives - such as the negatives you get when you have photographs developed. So, whenever you are dealing with negative numbers - think of them as simply being the opposite of positive numbers.

Adding

When you add two positive numbers e.g. 2 + 2 the answer will always be positive i.e. 4
When you add two negative numbers e.g. -2 + -2 the answer will always be negative i.e. -4 (this is like saying minus 2 degrees below zero plus another minus 2 degrees below zero)

Subtracting

When you subtract two positive numbers the answer could be positive e.g. 3 - 1 = 2 or negative! e.g. 3 - 7 = -4
Have a look at this on the number scale to see how it works:
………….-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6………..

Count backwards (right to left) from 3 through the purple numbers for 7 steps (call the gap between 3 and 2 a step, then the one between 2 and 1 and the one between 1 and 0 etc.) and you end up with the answer -4.

What is -7 + 3? Look at the number scale again and count 3 to the right from -7 and you end up with -4.

In other words -7 + 3 is exactly the same as 3 - 7.
-3 - 2 means the same as -3 + -2. By moving another 2 places to the left of the scale from -3 we get the answer as -5.

Now for the funny bit…..
What is -3 - -2 (minus 3 minus minus 2)? this is nearly always written as -3 - (-2) where the brackets just make it easier for people to see that you have written two minus signs - - and don't just have a dodgy pen and only intended to write a single minus.

Back to the question -3 minus -2 again - Think of opposites - you know that -3 -2 moves two to the left of the number scale and gives the answer -5. So -3 - (-2) being opposite must move two to the right of the number scale giving the answer -1.
Secret: If ever you see two minus signs together - treat them as a plus (positive) number e.g. -3 -(-2) is exactly the same as -3 + 2!


Back to the question -3 minus -2 again - Think of opposites - you know that -3 -2 moves two to the left of the number scale and gives the answer -5. So -3 - (-2) being opposite must move two to the right of the number scale giving the answer -1.
Secret: If ever you see two minus signs together - treat them as a plus (positive) number e.g. -3 -(-2) is exactly the same as -3 + 2!

Multiplying

There's another secret coming up here which is surprisingly similar to the one you've just learnt - wait for it.
Firstly, a negative number multiplied by a positive number is always negative e.g. -3 x 2 = -6 and likewise 3 x -2 = -6.
-3 x 2 is like saying "I'm at -3 on the number scale and need to go twice as far as -3 to get the answer - so you move on another -3 (to the left of the scale) giving you the answer -6.
Now, when a negative number is multiplied by a negative number the answer is always positive.
Secret: A minus number times a minus number always gives a plus number (e.g. -3 x -4 = 12, -10 x -3 = 30).

Dividing

Here the technique is the same as multiplying. A negative number divided by a positive number gives a negative number e.g. -6/3 = -2.
Also a positive number divided by a negative number also gives a negative numbere.g. 6 / -3 = -2.
So what do you think a negative number divided by a negative number is?
That's it you've guessed it (if you've understood the section on multiplying). Negative divided by negative gives positive.
Secret: A minus number divided by a minus number gives a plus number (e.g. -6/-3 = 2)

The bit most people forget

If you see two minus numbers together when multiplying or dividing the answer will always be plus.
When a minus number is subtracted from another minus number, the two minuses - - should be treated as if they were +.
"TWO MINUSES ALWAYS MAKE A PLUS"

Earlier we were talking about opposites - did you notice that it isn't just the positive and negative numbers which are opposite?
Subtraction is the opposite of Addition and
Division is the opposite of Multiplication