Integers

Karyn Carson

Adding and subtracting integers (positive and negative numbers) can be difficult to understand. There are no ‘rules’ to remember so we need to construct a scenario to help us make sense of it. You can use this idea to help you any time you find yourself not knowing what to do when adding and subtracting integers.

Let’s go on a hot air balloon ride. What can we do to go higher? What can we do to lower the balloon? We’re going to use a number line to track our progress.

To rise: ADD helium

SUBTRACT sandbags

To drop: ADD sandbags

SUBTRACT helium

For our purposes, we’ll consider helium as positive integers and sandbags as negative integers.

Let’s begin with 8 and add 4 helium …

What happens when you add helium to a balloon? Where will you end up?

Use your number line and balloon to find the answer.

Yes! If you add 4 helium to 8, the balloon rises on the number line to 12.

The equation for this scenario looks like this:

8 + 4 = 12

Now, let’s take away 4 sandbags. What happens to the balloon? Does it rise or fall? What is the result? Let’s look at the equation:

8 – (-4) = 12

What do you notice about both of these situations? How are adding helium and subtracting sandbags alike?

Yes, they achieve the same result. Let’s try a few. Rewrite each subtraction expression as an addition expression:

1. 17 – (-9)

2. 5 – (-6)

3. 0 – (-12)

4. 3 – (-10)

5. 10 – (-3)

Now, let’s add 4 sandbags to 8. What happens to the balloon this time? What is the result?

If you add 4 sandbags to 8, the balloon drops on the number line and the result is 4. The equation for this is:

8 + (-4) = 4

What’s another way that you can achieve the same result? Write your response using both the balloon example and as an equation.

Take away 4 helium from 8.

8 – 4 = 4

How are adding sandbags and subtracting helium alike?

Use this information to rewrite each addition expression as a subtraction expression:

1. 4 + (-5)

2. 18 + (-10)

3. 37 + (-2)

4. 52 + (-45)

5. 8 + (-17)

Now, let’s use our number lines to find these answers:

1. If you start at 4 and either add 5 sandbags or subtract 5 helium, where will your balloon land on the number line?

2. 18 minus 10 is 8.

3. 37 minus 2 is 35.

4. 52 minus 45 is 7.

5. 8 minus 17 is -9.

How do you know that the difference in #5 will be negative?