How do you multiply and divide negative numbers?

Multiply/divide them as if they were positive, then add a negative symbol if the two numbers had different signs.

How do you add and subtract negative numbers?

Use a number line. Move to the right if adding a positive number or subtracting a negative number. Move to the left is subtracting a positive number or adding a negative number.

What is a negative number?

A negative number is a number that is less than zero.

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Chapter overview

Learning goals

Maths

Negative numbers: Add, subtract, multiply, divide

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Summary

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Negative numbers: Add, subtract, multiply, divide

In a nutshell

Negative numbers are numbers that are less than zero. It's possible to add, subtract, multiply and divide with them.

Adding and subtracting negative numbers

To add and subtract negative numbers, it is best done with a number line.

Maths; Types of numbers; KS3 Year 7; Negative numbers: Add, subtract, multiply, divide

Key things to know about adding and subtracting with negative numbers

Move to the left to subtract.
Move to the right to add.
Subtracting a negative number is the same as adding a positive number.

Example 1

What is $-4+5$ ?

Start off at $-4$ on the number line, then move $5$ steps to the right.

[asset: number line]

Moving $5$ steps to the right ends up at $1$ .

$\underline{-4+5=1}$

Example 2

What is $10-(-5)$ ?

Subtracting a negative number is the same as adding a positive number. Therefore:

$10-(-5)=10+5=15$

$\underline{10-(-5)=15}$

Multiplying and dividing negative numbers

To multiply and divide negative numbers, multiply them as if they were positive numbers. If the two numbers have different signs (so if one is positive and the other is negative), then add a negative symbol to the answer.

Example 3

What is $-5\times-7$ ?

Multiply the two numbers together as if they were both positive:

$5\times7=35$

Since both numbers have the same sign (they are both negative), there is no need to change the sign of the answer.

$\underline{-5\times-7=35}$

Example 4

What is $100\div-10$ ?

Divide the two numbers as if they were both positive:

$100\div10=10$

The numbers have opposing signs - one is negative and one is positive. Hence, the answer will be negative.

$\underline{100\div-10=-10}$

Negative numbers: Add, subtract, multiply, divide

In a nutshell

Negative numbers are numbers that are less than zero. It's possible to add, subtract, multiply and divide with them.

Adding and subtracting negative numbers

To add and subtract negative numbers, it is best done with a number line.

Key things to know about adding and subtracting with negative numbers

Move to the left to subtract.
Move to the right to add.
Subtracting a negative number is the same as adding a positive number.

Example 1

What is $-4+5$ ?

Start off at $-4$ on the number line, then move $5$ steps to the right.

[asset: number line]

Moving $5$ steps to the right ends up at $1$ .

$\underline{-4+5=1}$

Example 2

What is $10-(-5)$ ?

Subtracting a negative number is the same as adding a positive number. Therefore:

$10-(-5)=10+5=15$

$\underline{10-(-5)=15}$

Multiplying and dividing negative numbers

Example 3

What is $-5\times-7$ ?

Multiply the two numbers together as if they were both positive:

$5\times7=35$

Since both numbers have the same sign (they are both negative), there is no need to change the sign of the answer.

$\underline{-5\times-7=35}$

Example 4

What is $100\div-10$ ?

Divide the two numbers as if they were both positive:

$100\div10=10$

The numbers have opposing signs - one is negative and one is positive. Hence, the answer will be negative.

$\underline{100\div-10=-10}$

Want to find out more? Check out these other lessons!

Negative numbers

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Frequently Asked Questions (FAQ)

FAQs

Question: How do you multiply and divide negative numbers?

Answer: Multiply/divide them as if they were positive, then add a negative symbol if the two numbers had different signs.
Question: How do you add and subtract negative numbers?

Answer: Use a number line. Move to the right if adding a positive number or subtracting a negative number. Move to the left is subtracting a positive number or adding a negative number.
Question: What is a negative number?

Answer: A negative number is a number that is less than zero.

Theory

Exercises

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Negative numbers: Add, subtract, multiply, divide

Negative numbers: Add, subtract, multiply, divide

In a nutshell

Adding and subtracting negative numbers

Key things to know about adding and subtracting with negative numbers

Example 1

Example 2

Multiplying and dividing negative numbers

Example 3

Example 4

Negative numbers: Add, subtract, multiply, divide

In a nutshell

Adding and subtracting negative numbers

Key things to know about adding and subtracting with negative numbers

Example 1

Example 2

Multiplying and dividing negative numbers

Example 3

Example 4

Want to find out more? Check out these other lessons!

Now you’ve read the summary, have a go at the exercises!