# News & Events

# Adding and Subtracting Integers

- July 27, 2017
- Posted by: Proodu Learning
- Category: Number System Operations

Adding and subtracting integers may appear or sound like a difficult task, but that is usually only the case at first. After understanding what we actually are doing when we add and subtract integers, it becomes a much easier thing to do!

### What are integers?

**Integers** are basically whole numbers that can be positive or negative. **Positive**** numbers** are numbers that are greater than zero. A symbol that may hint at whether a number is positive is the addition symbol (+). That is because these numbers are often giving, like positive people! **Negative numbers** are numbers that are less than zero. These numbers are usually after a minus symbol (-). That is because these numbers often take away from other numbers.

Test your understanding by guessing whether the integers below are greater or less than zero.

- -31
- 400
- 2,507
- -10
- -23
- 86
- -9000

### How do you add integers?

Adding integers is actually an easy thing to do! You probably already know how to add some integers. For example, can you add 4 and 5? If you got 9, then you’re half way there! If not, practice adding these positive integers.

The secret to adding integers is understanding the breakdown of a math problem. Math is all about changing amounts. When we find the sum of 1 and 1, we get 2. How can we show that visually? Well, the most common and probably easiest way is to use a number line. Check the video below for an example.

The other half to adding integers is adding to negative numbers. Adding to negative numbers the same as giving, or making something more positive. Let’s begin by exploring a basic math fact. Try the example problems below to see if you’ve got it!

### How do you subtract integers?

Luckily for you, if adding integers have been a breeze, then so should subtracting them. It is the exact opposite of addition. Instead of moving to the right on the number line as we did with addition, we must move to the left. Think of the plus and minus signs as directions!

+ –> move to the right

– –> move to the left

Try the example problems below to see if you’ve got it!

### Adding and Subtracting Negative Integers

Up to this point, we have focused on adding and subtracting positive integers. What this means is the integer that follow the operation symbol has always been a positive integer. Let’s explore what happens when there is another negative involved.

Do you remember learning about the commutative property? The **commutative property** states that we can write some expressions in two ways, such as:

Even though the numbers are reversed, they still add up to be the same as they would before. Since we can do this with addition, we can do the same with other examples. For example:

When rewritten, the problem should look more familiar. We solved problems like those earlier! And with that, you can easily add negatives to any number. If that doesn’t help, there is one more way to make adding negative number a little easier. Adding a negative number is the same process as subtracting a positive number! Here’s an example of what I mean:

That’s right! And have you figured out the answer yet? Yep, it’s 4. The answer was lying right in front of us the entire time. Don’t worry, it isn’t meant to be obvious the first time you see it. Here’s a few more examples:

See? Adding negative integers aren’t all that bad. See if you can use the tricks to solve the problems below:

The last case we have is subtracting negative integers from negative integers. When we try to subtract a negative number, the opposite happens: we add a positive one! Here’s an example of what I mean:

As the diagram shows, it becomes an addition problem, with the answer 1. Here’s a few examples:

Time to put your new math skills to the test! Try the problems below: