# Calculating with integers

**Negative numbers**

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.

For example,

**–4** **> –9**

**–4 ‘is greater than’ –9**

**Adding integers**

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

**Subtracting integers**

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:

Note:

- 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.