Explore Arithmetic operations

One of the first things in math that we learn is counting. We count fingers, toys, apples, and oranges. When we count, we’re actually adding $$1$$ to the number we have already. Then we learn how to add more than just one at a time. This is what we call adding whole numbers: $$2+3=5$$.

But what if one of the things we’re counting is negative? Well, that’s when we don’t add whole numbers anymore — that’s when integers come into the picture!

## What does it mean to add integers?

Adding integers means performing addition over a set of integer numbers. An integer is any number from a set of whole numbers and their additive inverses – the numbers with the same absolute value but an opposite sign:

$$\{\ldots-3,-2,-1,0,1,2,3,\ldots\}$$

‘’Wait… what is the absolute value of a number?!’’

Good question! The absolute value of a number is that same number, but without the sign in front of it. Why? Because the absolute value actually shows us what the distance is from that number to $$0$$ on the number line. For example, the absolute value of $$|-4|=4$$. That’s the distance from $$-4$$ to $$0$$ on the number line, $$4$$ units:

The first summand (a number we want to add) tells us where to start on the number line. The sign on the second summand will tell us which way to move on the number line. If it’s positive, we count moving right. If it’s negative, we count moving left. The absolute value of the second summand is just the number without its sign.

### Why is adding integers so useful?

Besides the fact that adding integers is a skill we need in order to learn more about math, there are many real-life problems it can help us solve! For example, if a fish is swimming $$14$$ feet below sea level, and then tries to reach the surface and moves $$6$$ feet up, at what depth is it located now? Well, that problem can be solved by adding integers. The fact that the fish is $$14$$ feet below the sea level can be represented by the integer $$-14$$ and the fact that it moved up means we need to add $$6$$. Now, it all comes down to a simple math problem of adding integers:

$$-14+6$$

## How to add integers

Now that we understand what integers are and why they’re useful, it’s time to see them in action! Let’s walk through a problem together:

### Example 1

$$-5+3$$

Determine the absolute value of each number:
$$|-5|=5$$
$$|3|=3$$
Notice that the negative number has a greater absolute value, so keep the sign of $$-5$$ and subtract the smaller absolute value from the larger:
$$-(5-3)$$
Subtract the numbers inside the parentheses:

$$-2$$

### Example 2

This might seem like the same example, but it actually isn’t!

$$-5+(-3)$$

Notice that here we need to add two negative numbers! Remember, to factor out a term from an expression means to extract that term from all the terms in the expression. So, factor out the negative sign:
$$-(5+3)$$
Add the numbers inside the parentheses:

$$-8$$

That wasn’t so bad, right? Now that we’ve walked through detailed examples, let’s review the overall process so you can learn how to use it with any problem:

## Study summary

1. Keep the sign of the number with the larger absolute value  and subtract the smaller absolute value from the larger.
2. Subtract the numbers.

## Try it yourself!

Practicing math concepts like this one is a great way to prepare yourself for the math journey to come. So, when you’re ready, we’ve got some practice problems for you!

1. $$-15+8$$
2. $$-5+7$$
3. $$-9+1$$
4. $$-6+9$$

Solutions:

1. $$-7$$
2. $$2$$
3. $$-8$$
4. $$3$$

If you’re still struggling with the solving process, that’s totally okay! Stumbling a few times is good for learning. If you do get stuck or lost, scan the problem using your Photomath app and we’ll walk you through it.

Here’s a sneak peek of what you’ll see:

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