An Integer is a positive or negative whole number and includes zero.
For example, –5 is an integer.
–5 is read as ‘negative five’.
This can also be written as –5.
It is 5 less than 0.
This is phrased as ‘zero minus five equals negative five’.
Points to note:
- the “-” sign can be used to denote subtraction
- the “-” sign can be used to denote a negative number, e.g -5 “negative five”
- The “+” sign can be used for positive numbers but this is not required.
Integers on a number line
Positive and negative integers are shown on the line below.
The number line can then be used to compare integers.
–4 > –9
–4 ‘is greater than’ –9
Use the number line below to help with adding positive and negative integers.
–3 + 6 = 3
A positive integer is added to move forwards up the number line.
A negative integer is to move backwards down the number line.
–2 + –3 is the same as –2 – 3
We can use a number line to help us subtract positive and negative integers.
- when adding a negative number you move backwards down the line
- this can be a negative or positive depending on where you start
- adding a negative number can be the same as subtractive a positive value of that number
4 – 7 = –3
To subtract a positive integer we move backwards down the number line.
6 – 9 is the same as 6 – +9
How is the number line used to work out 6 – 9?
3 – –6 = 9
A negative integer is subtracted to move forwards up the number line.
3 – –6 is the same as 3 + 6
Adding and subtracting integers
- When adding a positive integer you move forwards up the number line.
- When adding a negative integer you move backwards down the number line.
a + – b is the same as a – b
- When subtracting a positive integer you move backwards down the number line.
- When subtract a negative integer you move forwards up the number line.
a – – b is the same as a + b
Rules for multiplying and dividing
The following rules should be considered when multiplying negative numbers:
Dividing is the inverse operation to multiplying.
The following rules should be considered when dividing negative numbers:
- When multiplying or dividing two numbers with different signs – always negative
- When multiplying or dividing two numbers with the same sign – always positive
Using a calculator
We can enter negative numbers into a calculator by using the
sign change key:
–56 ÷ –5 can be entered as:
The answer will be displayed as -61.