When adding and subtracting integers I think you will agree with me when I say:

A lot of students find it difficult – especially the addition and subtraction of negative numbers.

But is it?

**I cannot emphasize this enough:**

Students with a better understanding of what integers are and know the key points to remember, do better than students who don’t.

In this post, I am going to show you how you can easily add and subtract integers with confidence.

So…

### What are integers and how do we add and subtract them?

Integers can be found on a number line. They are negative and positive numbers, including zero.

….., -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …..

The further you go to the right of zero the bigger the number gets, and the further you go to the left of zero, the smaller the number becomes. For example, -5 is smaller than -2. This can be written as -5 < -2, and reads -5 is less than -2.

### Here are the key points to remember when working with integers.

- Zero is an integer that is neither negative nor positive.
- Integers above zero are known as counting numbers. They are, 1, 2, 3, 4, 5, ….
- Positive integers including zero are known as whole numbers. They are, 0, 1, 2, 3, 4, 5, 6, ….
- Integers below zero are known as negative numbers. Example, …. -5, -4, -3, -2, -1
- The sign of a number appears before the number. Example, -12 means 12 below 0 and 12 means 12 above 0
- A number written without a sign is a positive number. Example, 7 is +7.
- You can use a number line to add and subtract integers – move right when adding, and left when subtracting.

Example (1) -3 + 2 = -1 You start at -3 and move 2 places to the right.

Example (2) 1 – 4 = -3 You start at 1 and move 4 places to the left.

Example (3) -2 – 2 = -4 You start at -2 and move 2 places to the left.

**Did you know…**

You can use your knowledge of temperature when adding and subtracting integers. For example, if you choose any number on the number line, the further you move to the left of that number, the colder it gets. Example, -5 is smaller and colder than -4, and -6 is smaller and colder than all integers to the right of -6, such as -5, -4, -3, and so on.

**How can you actually use your knowledge of temperature?**

Let us consider an ice cube represented by the integer -1. If the container has 4 ice cubes, that means 4 ice cubes have been added to the container. That can be written as (-1) + (-1) + (-1) + (-1) = -4

The brackets have been used to show the type of numbers being added – negative numbers.

It is worth remembering that adding a negative number gives the same result as subtracting the absolute number.

i.e. + (-) means –

So (-1) + (-1) + (-1) + (-1) = -4 can be written as -1 – 1 – 1 – 1 = -4

**Now…**

### What happens when you subtract a negative integer?

Let us consider the container with the four ice cubes again (-4). If we take away (subtract) one of the ice cube (-1), this calculation can be written as (-4) – (-1) or -4 – -1.

The result will be -3 because there are three ice cubes remaining and each ice cube is represented by -1.

It is worth remembering that subtracting a negative number gives the same result as adding the absolute number.

i.e. – (-) means +

So (-4) – (-1) can be written as -4 + 1 = -3

### Another method used to explain the addition and subtraction of integers is pattern spotting.

Consider the calculations below for adding integers.

2 + 3 = 5

2 + 2 = 4

2 + 1 = 3

2 + 0 = 2

2 + -1 = 1

2 + -2 = 0

2 + -3 = -1

You may spot the pattern of the numbers being added to 2 decreasing by 1 each time and so are the results.

+ – means –

2 + -1 can be written as 2 – 1 = 1

2 + -2 can be written as 2 – 2 = 0

2 + -3 can be written as 2 – 3 = -1

**That’s not all…**

Consider the calculation below for subtracting integers.

2 – 3 = -1

2 – 2 = 0

2 – 1 = 1

2 – 0 = 2

2 – -1 = 3

2 – -2 = 4

2 – -3 = 5

You may spot the pattern of the numbers being subtracted from 2 decreasing by 1 each time and the results increasing by 1 each time.

– – means +

2 – -1 can be written as 2 + 1 = 3

2 – -2 can be written as 2 + 2 = 4

2 – -3 can be written as 2 + 3 = 5

In summary, there are several methods used to explain the addition and subtraction of integers. We have covered some of the methods here, and hope you have found this post useful. It was written by Key Stage Tutors a one-to-one tuition website providing online tutoring in several academic subjects. You can see a blog on multiplying and dividing integers by clicking here.