How to Add Negative Integers

Learn a quick tip for using the number line and putting down your calculator.

Jason Marshall, PhD ,
February 6, 2010
Episode #004

Today’s article will walk you through the first steps of kicking your calculator dependency. This isn’t something we can accomplish in a single article, so we’ll be revisiting this topic periodically. Today, we’re kicking things off by using a number line, instead of a calculator, to help you keep your signs straight.

Review of Integers

But before we start working to break that calculator habit, let’s briefly review what we talked about last time. The most important thing to take away was the idea that combining negative whole numbers with the natural numbers gives us the very important group of numbers known as integers. These integers can be arranged on a number line with big negative ones extending out indefinitely to the left, zero in the middle, and big positive ones extending out forever to the right. At the end of the article I asked if any integers exist that are neither positive nor negative. What do you think? If you take all the positive and negative integers off the number line, are there any integers left? How about that strange one right in the middle? Yep, that’s the one: zero.

How to Understand the Number Line

Okay, how about the other question? Did you figure out how to put the integers 101, -1, 32, and -2010 in order from smallest to largest? Once you understand the number line and how positive and negative numbers relate to each other, this shouldn’t be too hard. The number -2010 is the smallest since it’s the most negative, then comes -1, then 32, and finally 101 is the largest. But perhaps you’re thinking: How can -2010 be the smallest!? It’s a pretty big number...it has four digits!

Well, here’s a quick and dirty tip to help you keep the relative size of numbers straight. Think about the number line again. Any number to the left of another on the number line must be the smaller of the two. Even though it might be a big number—in that it might have a lot of digits like negative one-trillion—it’s still smaller-than any number to the right of it. Even a seemingly puny one-digit number like zero.

How to Kick Your Calculator Dependency

Okay, with all that covered, let’s talk about our first calculator dependency kicking technique. This one is aimed at making addition of positive and negative integers easier. Let’s say you need to solve a problem like -46+16. Your first instinct might be to go grab your calculator and start punching numbers. Yes, that should give you the right answer, but you run the risk of not understanding the very important question of why it gave you the right answer. And, if you don’t understand “why,” how will you ever know if you’ve made some egregious error, resulting in sharing an embarrassingly ridiculous—and wrong—answer with everybody. Avoid this risk and learn how to do the problem in your head instead. That way you’ll know when something is fishy with a result.


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