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Adding and subtracting positive integers

This topic is relevant for:

Here we will learn about **adding and subtracting** **negative numbers** including what negative numbers are and how to add and subtract them.

There are also negative numbers worksheets and exam questions at worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Negative numbers** are any numbers less than zero and that have a negative sign (−) in front of them.

Numbers greater than zero are referred to as **positive numbers**. If there is no sign in front of a number the number is positive.

On the **number line** below the numbers in orange are negative values and the blue numbers are positive values:

Just like you can add and subtract positive numbers, you can do the same with negative numbers.

When adding and subtracting negative numbers use a number line:

**If you are adding, move to the right of the number line.**

**If you are subtracting, move to the left of the number line**.

When you have two signs next to each other:

**If the signs are the same replace with a positive sign**.

**If the signs are different, replace with a negative sign.**

In order to add and subtract negative numbers:

- If you have two signs next to each other, change them to a single sign.
**If the signs are the same replace with a positive sign (+)**.**If the signs are different, replace with a negative sign (−)**. - Circle the first number on the number line.
- Use the number line to add or subtract your numbers.
**If you are adding, move to the right of the number in step 2 (→)**.**If you are subtracting, move to the left of the number in step 2 (←)**. - Write your final answer.

Get your free adding and subtracting negative numbers worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free adding and subtracting negative numbers worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREE\[ -4+7 \]

**If you have two signs next to each other, change them to a single sign.****If the signs are the same replace with a positive sign (+)**.**If the signs are different, replace with a negative sign (−)**.

In this case you do not have two signs next to each other.

2**Circle the first number on the number line**.

The first number in the question is

3**Use the number line to add or subtract your numbers**.**If you are adding, move to the right of the number in step 2 (→)**.**If you are subtracting, move to the left of the number in step 2 (←)**.

In this case we are adding the

4**Write your final answer**.

\[-4 + 7 = 3\]

\[ -2+(-3 )\]

**If you have two signs next to each other, change them to a single sign.****If the signs are the same replace with a positive sign (+)**.**If the signs are different, replace with a negative sign (−)**.

In this case you have a plus and a minus next to each other.

Since the signs are different, replace with a minus sign (−):

\[-2 -3\]

**Circle the first number on the number line**.

The first number in the question is

**Use the number line to add or subtract your numbers**.**If you are adding, move to the right of the number in step 2 (→)**.**If you are subtracting, move to the left of the number in step 2 (←)**.

In this case we are subtracting

**Write your final answer**.

\[-2 + (-3) = -5\]

\[ -5-2 \]

**If you have two signs next to each other, change them to a single sign.****If the signs are the same replace with a positive sign (+)**.**If the signs are different, replace with a negative sign (−)**.

In this case you do not have two signs next to each other.

**Circle the first number on the number line**.

The first number in the question is

**Use the number line to add or subtract your numbers**.**If you are adding, move to the right of the number in step 2 (→)**.**If you are subtracting, move to the left of the number in step 2 (←)**.

In this case we are subtracting

**Write your final answer**.

\[-5 – 2 = -7\]

\[ -8-(-10) \]

**If you have two signs next to each other, change them to a single sign.****If the signs are the same replace with a positive sign (+)****If the signs are different, replace with a negative sign (−)**

In this case you have a minus and a minus next to each other.

Since the signs are the same, replace with a plus sign (+)

\[-8 + 10\]

**Circle the first number on the number line**.

The first number in the question is

**Use the number line to add or subtract your numbers**.**If you are adding, move to the right of the number in step 2 (→)**.**If you are subtracting, move to the left of the number in step 2 (←)**.

In this case we are adding

**Write your final answer**.

\[-8 – (-10) = 2\]

\[ 7-8 – (-5) \]

**If you have two signs next to each other, change them to a single sign.****If the signs are the same replace with a positive sign (+)**.**If the signs are different, replace with a negative sign (−)**.

In this case you have a minus and a minus next to each other.

Since the signs are the same, replace with a plus sign (+)

\[7 – 8 + 5\]

**Circle the first number on the number line**.

The first number in the question is

**Use the number line to add or subtract your numbers**.**If you are adding, move to the right of the number in step 2 (→)**.**If you are subtracting, move to the left of the number in step 2 (←)**.

In this case we are subtracting positive

Now we are adding

**Write your final answer**.

\[7 – 8 – (-5) = 4\]

Alina had

Let’s start with

\[12 – 20 \]

**If you have two signs next to each other, change them to a single sign.****If the signs are the same replace with a positive sign (+)**.**If the signs are different, replace with a negative sign (−)**.

In this case you do not have two signs next to each other.

**Circle the first number on the number line**.

The first number in the question is

**Use the number line to add or subtract your numbers**.**If you are adding, move to the right of the number in step 2 (→)**.**If you are subtracting, move to the left of the number in step 2 (←)**.

In this case we are subtracting

Because the scale on the number line below is in

**Write your final answer**.

\[12 – 20 = -8\]

She is overdrawn by £8.

**Greater negative does not mean a larger number**

A common error is to assume that the larger a negative number is, the bigger number is.

E.g.

Adding and subtracting negative numbers is part of our series of lessons to support revision on negative numbers. You may find it helpful to start with the main negative numbers lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

1. Work out: -6 + 10

-4

4

-16

16

2. Work out: -4 + -8

-12

12

4

-4

```
There is a + - together so change it to a -
-4 + - 8 = -4 - 8
```

3. Work out: -9 – 12

-3

3

21

-21

4. Work out: -15 – (-6)

-21

-9

9

21

```
There is a - - together so change it to a +
-15-(-6) = -15+6
```

5. Work out: -7 + (-8) -5+2

-2

-8

-18

-12

```
There is a + - together so change it to a -
-7+(-8)-5+2 = -7 -8 -5 +2
```

6. At 5 am in the morning, the temperature in Cambridge was -9 ℃. By 10 am the temperature had risen by 11 ℃. What was the new temperature?

20^{\circ}\text{C}

-20^{\circ}\text{C}

-2^{\circ}\text{C}

2^{\circ}\text{C}

`The calculation we need to do is -9+11 `

The table shows the temperature in Watford at different times of the day.

Time of the Day | Temperature (℃) |

2am | -3 |

4am | 0 |

6am | 2 |

8am | 6 |

(a) Write down the lowest temperature.

(b) Find the difference between the warmest and the coldest temperature readings.

**(3 marks)**

Show answer

−3

**(1)**

Identifying the warmest and coldest temperatures, 6 and -3

**(1)**

6−3=9

**(1)**

2. Sarah has the following 6 cards:

She is going to choose 2 cards and subtract them.

(a) What is the largest possible number she can make?

(b) Sarah now decided to add the numbers rather than subtract them. What is the smallest possible number she can make?

**(4 marks)**

Show answer

a) for identifying 3 or −8 or 3− (−8) seen

**(1)**

correctly subtracting two numbers or 11 seen

**(1)**

b) for identifying −7 or −8

**(1)**

correctly adding two numbers or −15 seen

**(1)**

3. Mr. and Mrs. Smith had £ 156.78 in their bank account. At the end of the month they had to pay 4 bills. They paid the telephone bill of £ 67.20 , utilities of £ 34.78 , car insurance £ 78.24 , and credit card bill of £ 144 . How much were the Smiths overdrawn?

**(3 marks)**

Show answer

Finding the sum of the 4 bills

(£324.22)

**(1)**

Subtracting the cost of the four bills from the balance in the bank account

(£156.78-£324.22)

**(1)**

£ 167.44

**(1)**

You have now learned how to:

- Add and subtract integers both positive and negative
- Use negative numbers in context and calculate intervals across 0

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