Mr F

1
Mr Fs Maths Notes

• Number
• 8. Negative Numbers

2
8. Negative Numbers
WARNING If you are not concentrating, negative
numbers can trip up the best of mathematicians.
So have a glass of water, shake all other
thoughts out of your head, sit down, take a deep
breath, and lets begin
The Number Line The key to negative numbers is
the number line. Now, I like to think of the
number line going up and down, so when you add
you go up, and when you subtract, you go down.
Kind of like a thermometer. If you ever find
yourself stuck or unsure about a negative number
question, just draw yourself a very quick number
line, count the spaces with your finger, and you
will be fine. I still do this, and Im well,
quite a bit older then you.
7
4 3 2 1 0 -1 -2 -3
6
5
4
3
2


1
0
- 1
- 2
- 3
- 4
- 5
- 6
3
Adding and Subtracting when the Signs are NOT
Touching Where people seem to go wrong with
negative numbers is that they learn the rule that
two minuses make a plus. Now, this rule is a good
one, but must only be used when two signs ( or
-) are touching. If no signs are touching, I
would just use this rule
Rule If no signs are touching, use a number
line (on paper or in your head), or think about
money!
Example 1
Example 2
Example 3
7
2 - 7
-4 6
-1 - 4
6
5
Number Line put your finger at 2 and move down 7
places
Number Line put your finger at -4 and move up 6
places
Number Line put your finger at -1 and move down
4 places
4
3
2

Money if I have 2 in my bank and someone takes
away 7, then how much do I have?
Money if I have -4 in my bank (I am in debt)
and someone gives me 6, then how much do I have?
Money if I have -1 in my bank (I am in debt)
and someone takes away 4, then how much do I
have?

1
0
- 1
- 2
2 7 -5
-4 6 2
-1 - 4 -5
- 3
- 4
- 5
- 6
4
Now both these methods still work when the
numbers become harder and the number line becomes
too big to draw
Example 4
Example 5
56
56 - 89
-102 217


Number Line imagine your finger is as 56. How
far must you go down to get to zero?... 56
spaces, right? And so, how much further down do
you still have to go? another 33 spaces!
Number Line imagine your finger is as -102. How
far must you go up to get to zero?... 102 spaces,
right? And so, how much further up do you still
have to go? another 115 spaces!
115
56
115
0
0
33
102
Money if I have 56 in my bank and someone takes
away 89, then how much do I have?
Money if I have -102 in my bank and someone
gives me 217, then how much do I have?
- 33
- 102
56 89 -33
-102 217 115
5
Adding and Subtracting when the Signs ARE
Touching Okay, now its time for our rule
Rule If two signs are touching (s or s next
to each other), then replace the two signs with
one sign using these rules and - - -
and - and - and -
Example 1
Example 2
Example 3
Example 4
-4 -8
5 - -6
-22 - - 9
-6 - 10
Have you spotted the touching signs?... Using our
rule, we can change and - to - So, our sum
becomes
Have you spotted the touching signs?... Using our
rule, we can change - and - to So, our sum
becomes
Have you spotted the touching signs?... Using our
rule, we can change - and - to So, our sum
becomes
Have you spotted the touching signs?... I hope
not, because there arent any! The two minuses
are NOT touching So our sum stays the same and we
do it using either of our methods
-4 - 8
5 6
-22 9
Which is pretty easy using either number lines or
money.
Which is pretty easy however you do it!
Which is pretty easy using either number lines or
money
-4 -8 -12
5 - -6 11
-22 - -9 -13
-6 - 10 -16
6
Multiplying and Dividing As was the case with
fractions, multiplying and dividing with negative
numbers is a little bit easier than adding and
subtracting, but you still have to concentrate!
Rule Do the sum as normal, ignoring the plus
and minus signs and write down the answer
Then, carefully count the number of minus signs
in the question. If there is one the
whole answer is negative, if there are two the
answer is positive, if there are three the answer
is negative, four means positive, and so on
Example 1
Example 2
Example 3
Example 4
-20 4
-6 x -9
-3 x -2 x -5
Do the sum as normal, ignoring the minus signs
Do the sum as normal, ignoring the minus signs
Do the sum as normal, ignoring the minus signs
Do the sum as normal, ignoring the minus signs
20 4 5
6 x 9 54
3 x 2 x 5 30
Count the number of minus signs in the question
1!
Count the number of minus signs in the question
2!
Count the number of minus signs in the question
3!
Count the number of minus signs in the question
2!
One minus makes the whole answer negative So
Two minuses makes the whole answer positive So
Three minuses makes the whole answer negative So
Two minuses makes the whole answer positive So
-20 4 -5
-6 x -9 54
-3 x -2 x -5 -30
7
Tricky Questions involving Negative Numbers The
people who write maths exams are nasty. Just when
you think you have got a topic sorted, they chuck
in a right stinker. But do not panic. So long as
you remember the rules we have discussed here,
and you dont forget our old friend
BODMAS/BIDMAS, you will be fine!
Example 1
Example 2
Example 3
Now, BIDMAS says we must sort out the brackets
first
Now, BIDMAS says we must sort out the division
first
Now remember, even though we cant see any
brackets, they are hidden on the top and bottom
of the fraction
So now we have
Putting that back in the question, we have
So, the top gives us
And using our negative number rules, we should
get the answer of
Lets sort those two touching signs out
And from the bottom
-4
Using number lines, or money, we should get
Leaving us with
-7
2
8

• Good luck with your revision!