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?