Home > Pre-Algebra > Integers > Adding Integers

#### Introduction

Integers are just whole numbers. Knowing how to add them is one of the first things you learn in Math. 2 + 2 = 4 is an addition of integers.

Where it can get tricky is when you add integers with different signs, such as two negative integers. To do that, you need to follow a couple of additional steps.

#### Terms

Integer - A whole number (i.e. not a fraction or a decimal. 3 is an integer, 4.5 and 2/3 are not.)

## Lesson

How you add integers depends on whether you're adding two positives, two negatives, or a combination of positive and negatives.

### Positives

Adding two (or more) positive numbers is one of the first things you learn in Math. To do that, simply combine the two values to find the answer.

For example:

$8 + 7 = mathord{?}$

8 and 7 combined is 15, so that is the answer:

$8 + 7 = 15$

### Negatives

Adding two or more negatives is a little trickier. One way to think about it is to use absolute values. If you have two numbers that are both negative, convert them both to positives and add them.

For example:

$-19 + -5 = mathord{?}$

Use the absolute values of both numbers:

$|-19| = 19$

$|-5| = 5$

That gives us:

$19 + 5 = mathord{?}$

19 and 5 combine to make 24, so

$19 + 5 = 24$

However, we have to remember to add the negatives back in. We add a negative to the answer as well, giving us:

$-19 + -5 = -24$

### Mixed Positive and Negative

To combine positive and negative numbers, we can think of a number line. If we are adding numbers, we move to the right on the number line; if we are subtracting, we move to the left.

For example:

$-8 + 4 = mathord{?}$

Here we would imagine a number line, where we start at the point -8. Since we are adding, we need to move 4 places to the right. That will give us -4.

So, $-8 + 4 = -4$

If we take the sum:

$5 + -7 = mathord{?}$

Since adding a negative is the same as a subtraction, we can rewrite it as follows:

$5 - 7 = mathord{?}$

So we imagine a number line, and we're starting at +5. As we're subtracting, we move 7 places to the left, which gives us -2.

So, $5 + -7 = -2$

## Examples

$12 + -8$
Plot $12$ on a number line
Because the second number is negative, we move $8$ to the Left
Evelyn's initial account balance was \$-5. Later Evelyn deposited \$20 into the account. What was the final balance?
Plot $-5$ on a number line
Because the second number is positive, we move $20$ to the Right
$-4 + 6$
Plot $-4$ on a number line
Because the second number is positive, we move $6$ to the Right
Sophia deposited \$29 into she account. Later Sophia deposited \$20 more into the account. What was the total amount deposited?
Plot $29$ on a number line
Because the second number is positive, we move $20$ to the Right