Understanding Integers

While you may know that integers are both positive and negative numbers, can you solve problems with integers? Integers can be a stumbling block for some, but if you relate integers to something in the real world, they are a lot easier to understand.

Integers can be used to describe income and loss or the rise and fall of temperatures or heights. Here are a few problems involving integers and an explanation of how to solve them.

Addition of Integers
Suppose you borrowed $500 to buy an iPod and a stereo. You pay back $175 of the loan. How much do you still owe?

Now, I know you are going to say that you can solve this just by subtracting 175 from 500. You can. But knowing how to solve this with integers will give you an understanding of how integers work.

After borrowing $500, you were in debt, or in the negative. -500 represents the amount you borrowed. The amount you paid back is a positive number. It helped you get partially out of debt. You can represent this problem with the equation
-500 + 175 = -325

After paying off $175, you were still -325 in debt.
Adding a negative number and a positive number is the same as subtracting the two numbers and taking the sign of the greater number.

Let’s try another one.
Suppose the wind chill factor on a cold, winter day is -10. The weather forecast says that the wind chill factor will drop by 20 degrees overnight. What will the wind chill factor be after the drop?

Now, we have to use negative numbers because the temperature is a negative number. But adding these numbers is no more difficult than adding positive numbers.

A drop of 20 degrees means the temperature is getting colder. A drop is a negative number. You can represent this problem with the equation
-10 + -20 = -30

The wind chill factor will be -30 degrees after the 20 degree drop.
When you add two negative numbers, it’s the same as adding two positive numbers. Just put a negative sign on the answer.

Subtraction of Integers
You’ve find this explanation very short. You can write any subtraction problem as an addition problem.

-4 – +3 is the same as -4 + -3 (just switch the positive sign on the 3 with the subtraction sign).

10 – -6 is the same as 10 + 6. Two negatives in a row make a positive.

This is a stumbling block for some. It’s just something that you may have to take on faith. But, you can relate it to our language. If you say that you never not exercise, you mean that you always exercise. “never” and “not” are two negative words that, when used together, have a positive meaning. The same is true with numbers.

In your normal, daily routine, you will likely not run into the opportunity to multiply or divide integers. But, if you do, let me know. I’ll show you how to solve them! 😉