Home > Pre-Algebra > Integers > Subtracting Integers

## Subtracting Integers

#### Introduction

Subtracting integers means reducing the first value by the second amount in an equation. So in the equation:

$8 - 3 = ?$

We take 8, reduce it by 3, leaving us with 5. So, 8 - 3 = 5.

However, when we are working with negative values or a mixture of positive and negatives, things get a little more advanced.

## Lesson

The golden rule to follow with subtracting integers is to combine the signs before you move on with the equation. The rules for combining signs are:

1) Negative and negative = addition

2) Positive and positive = addition

3) Negative and positive = subtraction

So, if you have the following equation:

$10 - -3 = ?$

You would first combine the signs. Since you have two negative (-) signs together, you convert that to an addition sign, meaning the equation looks like this:

$10 + 3 = ?$

We can then solve, since $10 + 3 = 13$.

In the equation:

$16 + -4 = ?$

We can combine the signs. A negative and a positive sign together make a subtraction, so the equation looks like this:

$16 - 4 = ?$

$16 - 4 = 12$, so that is the solution.

So, just remember, if the two signs are the same (- and -, or + and +) then the result is +; if the two signs are different (- and +, or + and -) then the result is -.

## Examples

$12 - -4$
When subtracting a negative number, the minus signs cancel out
$12 - -4 = 12 + 4$
Plot $12$ on a number line
Because the second number is positive, we move $4$ to the Right
Addison was 54 inches tall on her fifth birthday. On her sixth birthday she was 64 inches tall. How much did she during the year?
Plot $54$ on a number line
Because the second number is negative, we move $64$ to the Left