Academic Skills Advice
Negative Numbers
A negative number is less than 0. To understand negative numbers better you might find it
easier to think about the temperature in a freezer or an overdrawn bank account.
For example, if you are overdrawn by £50 then you have -£50 in the bank. Remember the
minus (negative) sign is always in front of the number it is connected to.
You need to know how to perform all 4 rules (+, -, x and ÷) with negative numbers.
Adding and Subtracting
Examples:
9–3=6
12 – 8 = 4
20 – 5 = 15
These should be easy for you as you are used to
this sort of calculation.
Think about what “-“ means: it can be seen as the “difference” between 2 numbers, for
example:
9 – 3 = the difference between 9 and 3 = 6
12 – 8 = the difference between 12 and 8 = 4 etc
So, what if you are presented with a calculation such as:
𝟗 − (−𝟑) (9 take away minus (or negative) 3).
Let’s look at the difference between 9 and (−3):
10
9
8
7
6
5
4
3
2
1
There are 9 spaces
between 9 and 0.
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
© H Jackson 2010 / ACADEMIC SKILLS
There are another 3 spaces
between 0 and (−3).
The total distance between 9 and (−3) is 12.
An easy way to do this calculation (without using a diagram) is to
remember that 2 minus signs together can be replaced with a +.
e.g.
9 − (−3) = 9 + 3 = 12
1
Examples:
15 − (−4) = 15 + 4 = 19
22 − (−3) = 22 + 3 = 25
More Adding & Subtracting
When the 2 negative signs are not together you can just think about moving up and down
the number line. If you are adding (increasing) you move up the number line and if you
are subtracting (decreasing) you move down the number line.
Examples:
−5 + 7 = 2
−3 + 10 = 7
4 − 9 = −5
2 − 3 = −1
−2 − 5 = −7
(try it on the number line, start at −5 and add on (move up) 7)
(try it)
(notice that you end up with a negative number as you are taking
away more than you started with.)
(be careful with this one, the 2 minus signs are not together so
do not become +, this means start at −2 then go down 5.
Try it on the number line.
−8 − 10 = −18 (try it)
−11 − (−3) = −8 (this becomes −11 + 3, so start and -11 and move up 3)
Multiplying and Dividing
Let’s look at another (similar) rule about 2 minus signs becoming a +. This is used when
2 negative numbers are multiplied or divided.
The following is an important summary when using x and ÷ with negative numbers:
2 signs the same gives +
2 different signs gives –
+ve and +ve
-ve and -ve
+ve and -ve
-ve and +ve
⟹ +ve
⟹ +ve
⟹ -ve
⟹ -ve
Examples:
5 × 3 = 15
−5 × −3 = 15
−5 × 3 = −15
5 × −3 = −15
(if there is no sign it is a positive number)
(− × − becomes +)
(− × + becomes −)
(+ × − becomes −)
15 ÷ 3 = 5
−15 ÷ −3 = 5
−15 ÷ 3 = −5
15 ÷ −3 = −5
(− ÷ − becomes +)
(− ÷ + becomes −)
(+ ÷ − becomes −)
© H Jackson 2010 / ACADEMIC SKILLS
2