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Positive and Negative
numbers
Negative numbers
A positive or negative whole number, including zero, is
called an integer.
For example, –3 is an integer.
This can also be written as –3.
It is 3 less than 0.
0 – 3 = –3
Here the ‘–’ sign means
minus 3 or subtract 3.
Here the ‘–’ sign means
negative 3.
Integers on a number line
Positive and negative integers can be shown on a number line.
–8
–3
Negative integers
Positive integers
We can use the number line to compare integers.
For example,
–3 ‘is greater than’ –8
Adding integers
We can use a number line to help us add positive and
negative integers.
–2 + 5 = 3
-2
3
To add a positive integer we move forwards up the
number line.
Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
5 – 8 == –3
-3
5
To subtract a positive integer we move backwards down
the number line.
5–8
is the same as
5 – +8
Adding integers
We can use a number line to help us add positive and
negative integers.
–3 + –4 == –7
-7
-3
To add a negative integer we move backwards down the
number line.
–3 + –4 is the same as
–3 – 4
Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
3 – –6 = 9
3
9
To subtract a negative integer we move forwards up the
number line.
3 – –6
is the same as
3+6
Subtracting integers
We can use a number line to help us subtract positive and
negative integers.
–4 – –7 = 3
-4
3
To subtract a negative integer we move forwards up the
number line.
–4 – –7
is the same as
–4 + 7
Adding and subtracting
integers
To add a positive integer we move forwards up the
number line.
To add a negative integer we move backwards down the
number line.
a + –b is the same as a – b.
To subtract a positive integer we move backwards down
the number line.
To subtract a negative integer we move forwards up the
number line.
a – –b is the same as a + b.
Integer circle
sums
Rules for multiplying and
dividing
When multiplying
negative numbers remember:
+ × + = +
+ × – = –
– × + = –
– × – = +
Dividing is the inverse operation to multiplying.
When we are dividing negative numbers similar rules apply:
+ ÷
+ = +
+ ÷
– = –
– ÷
+ = –
– ÷
–
= +
Multiplying and dividing
integers
Complete the following:
–3 × 8 = –24
–36 ÷
42 ÷
–7 = –6
540 ÷ –90 = –6
–12 × –8 = 96
–7 × –25 = 175
47 × –3 = –141
–4 × –5 × –8 = –160
–72 ÷ –6 =
3 × –8 ÷ –16 = 1.5
12
9
= –4
Using a calculator
We can enter negative numbers into a calculator by using the
sign change key: (–)
For example:
–456 ÷ –6 can be entered as:
(–)
4
5
6
÷
(–)
6
=
The answer will be displayed as 76.
Always make sure that answers given by a calculator are
sensible.
Sums and products
What two integers have a sum of 2 and a product of –8?
Start by writing down all of the pairs of numbers that multiply
together to make –8.
Since –8 is negative, one of the numbers must be positive
and one of the numbers must be negative.
We can have:
–1 × 8 = –8
–1 + 8 = 7
1 × –8 = –8
1 + –8 = –7
–2 × 4 = –8
–2 + 4 = 2
or
The two integers are –2 and 4.
2 × –4 = –8
2 + –4 = –2
Sums and products