Adding and Subtracting Negatives

The opposite of a number is also called its additive inverse. The additive inverse is the number you have to add to it so that the sum is zero. So the additive inverse of 5 is -5. This is sometimes called the property of opposites.

If you add any number to its opposite, or additive inverse, the answer is always zero. For example:

$-989+989=0$

$6.5+(-6.5)=0$

$1+(-1)=0$

Once you know this, there are several ways you can think about adding and subtracting negative numbers.

Adding and subtracting negatives: The algebra tile method

Let the yellow tiles represent positive numbers and the red tiles represent negative numbers.

Example 1

The addition problem $5+(-2)$ can be represented as:

Group the two negative tiles with two of the positive tiles, zeroing them out.

Since $2+(-2)=0$ , these tiles disappear. We are left with 3 positive tiles.

Therefore, $5+(-2)=3$ .

When both numbers are negative, we have only negative tiles.

Example 2

The addition problem $-3+(-4)$ can be represented as

The result is simply 7 negative tiles.

Therefore, $-3+(-4)=-7$

Adding and subtracting negatives: The number line method

When you add a positive number, you move to the right on the number line.

When you add a negative number, you move to the left on the number line.

Example 3

Add $6+(-8)$ using a number line.

Start at 6 and move 8 units to the left.

So $6+(-8)=-2$

Subtracting a number is the same as adding its opposite. So subtracting a positive number is like adding a negative number - you move to the left on the number line.

Subtracting a negative number is like adding a positive number - you move to the right on the number line.

Example 4

Subtract $-4-(-7)$ .

Start at -4 and move 7 units to the right.

So $-4-(-7)=3$ .

Adding negative numbers without visual aids

Once you've become used to adding negative numbers using the algebra tile method or the number line method, you'll notice that adding a negative number is basically the same as performing a subtraction operation.

So these two problems $5+(-4)$ and $5-4$ are going to have the same answer.

Knowing this can help you perform the addition of negative numbers in your head.

Example 5

Solve the following addition problems involving negative numbers using your understanding of subtraction.

$8+(-3)$

Because we know that $8-3=5$ , you know that

$8+(-3)=5$

$259+(-384)$

Since we can work out that $259-384=-125$ , you know that $259+(-384)=-125$

What about when the negative number is larger than the positive number we are adding it to? Well, we know how to subtract a number that is larger than the number we are subtracting it from - we end up with a negative number.

Example 6

Solve the following addition problems involving negative numbers using our understanding of subtraction.

$8+(-15)$

Since we know that $8-15=-7$ , you know that

$8+(-15)=-7$

Subtracting negative numbers without visual aids

Once you've become used to subtracting negative numbers using the algebra tile method or the number line method, you'll notice that subtracting a negative number is basically the same as performing an addition operation. So the two problems $10-(-5)$ and $10+5$ are going to have the same answer.

Knowing this can help us perform the subtraction of negative numbers in your head.

Example 7

Solve the following subtraction problems involving negative numbers using your understanding of addition.

1. $7-(-3)$

Because we know that $7+3=10$ , we know that

$7-(-3)=10$

2. $157-(-90)$

Since we can work out that $157+90=247$ , we know that

$157-(-90)=247$

Topics related to the Adding and Subtracting Negatives

Multiplying and Dividing with Negatives

Operations with Negatives

Adding and Subtracting Fractions with Negatives

Flashcards covering the Adding and Subtracting Negatives

7th Grade Math Flashcards

Common Core: 7th Grade Math Flashcards

Practice tests covering the Adding and Subtracting Negatives

MAP 7th Grade Math Practice Tests

Common Core: 7th Grade Math Diagnostic Tests

Get help learning about adding and subtracting negatives

Adding and subtracting negative numbers takes a lot of practice. It can be confusing at first, and if your student is struggling with adding and subtracting negative numbers, they could use the help of a math tutor. An expert tutor can take the time your student needs to walk through each problem step by step until they understand the process of working with negative numbers. To learn how tutoring can help your student, contact the Educational Directors at Varsity Tutors today.