Positive and Negative numbers

Negative numbersA 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 = –3Here the ‘–’ sign means minus 3 or subtract 3.

Here the ‘–’ sign means negative 3.

Positive and negative integers can be shown on a number line.

Positive integersNegative integers

We can use the number line to compare integers.

For example,

–3–8

–3 ‘is greater than’ –8

Integers on a number line

Adding integersWe can use a number line to help us add positive and negative integers.

–2 + 5 =

-2 3

= 3

To add a positive integer we move forwards up the number line.

5-3

Subtracting integersWe can use a number line to help us subtract positive and negative integers.

5 – 8 == –3

To subtract a positive integer we move backwards down the number line.

5 – 8 is the same as 5 – +8

We can use a number line to help us add positive and negative integers.

To add a negative integer we move backwards down the number line.

–3 + –4 == –7

-3-7

–3 + –4 is the same as –3 – 4

Adding integers

3 – –6 =

3 9

= 9

We can use a number line to help us subtract positive and negative integers.

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 =

-4 3

= 3

To subtract a negative integer we move forwards up the number line.

–4 – –7 is the same as –4 + 7

Subtracting integers

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.

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.

a – –b is the same as a + b.

Integer circle sums

When multiplying negative numbers remember:

Rules for multiplying and dividing

Dividing is the inverse operation to multiplying.

When we are dividing negative numbers similar rules apply:

+ × + = +

–+ × = –

–+× =–

– +× =–

+ ÷ + = +

–+ ÷ = –

–+÷ =–

– +÷ =–

Multiplying and dividing integersComplete the following:

–3 × 8 =

42 ÷ = –6

× –8 = 96

47 × = –141

–72 ÷ –6 =

–36 ÷ = –4

÷ –90 = –6

–7 × = 175

–4 × –5 × –8 =

3 × –8 ÷ = 1.5

–24

–7

–12

–3

12

9

540

–25

–160

–16

Using a calculatorWe can enter negative numbers into a calculator by using thesign 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.

What two integers have a sum of 2 and a product of –8?

Sums and products

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 = –8 –2 × 4 = –8 or 2 × –4 = –8

–1 + 8 = 7 1 + –8 = –7 –2 + 4 = 2 2 + –4 = –2

The two integers are –2 and 4.

Sums and products