Adding Negative Numbers: It’s a sign!
Photo by Gage Walker on Unsplash
Sometimes, it’s okay to be negative. You’ll have to work with negative numbers when doing math for the GREs. If adding negative numbers always befuddled you, have no fear. With just a few minutes of review, you will know just how to handle them! I’m going to present you with a few different options for solving these problems: like a buffet, find the option you like and stick with it.
Adding when both numbers are negative:
When you add two negative numbers, the result will always be negative. Think of it this way: if you accidentally overdrew your bank account by 20 dollars (so the balance is -20), then you charged 10 dollars for lunch to that account, the balance would definitely still be negative.
Mathematically, it would look like this:
-20 + (-10) = -30
If you are adding two negative numbers, your equation is getting deeper into debt, so the result will be negative.
Try this one:
-39 + (-2) = ?
That’s right! It’s -41.
Adding when one number is negative:
300 + (-400) = ?
Option One - Intuitive Approach: Think of the numbers as money. Imagine you had 300 dollars in your bank account, and then you withdrew 400 dollars. Would you be in debt? Yes, by 100 dollars. That’s pretty intuitive. Mathematically, it would be:
300 + (-400) = -100
Option Two - Rewrite with Subtraction: Adding a negative number is the same as subtracting a positive number. Instead of adding -400, you could just subtract 400.
300 + (-400)
Can be rewritten as:
300 - 400
so 300 - 400 = -100
Option Three - Number line: (If you need a quick refresher on number lines, check out this post.) Start at the first number, then either hop right for positive numbers or left for negative numbers.
For 300 + (-400):
Start at 300 on the number line
Make 400 hops to the LEFT. That’s a lot of hops, so each green dashed arc represents 100 hops.
After 400 hops to the left (4 green dashed arcs) you land at -100
Examples:
Hopefully one of these options “speaks” to you! Let’s try two more problems:
3 + (-4) = ?
That’s right: -1. That makes sense, because there is more negative than positive in that equation (like some days in life). So you expect to end up with a negative.
Some days in life have more positive than negative, though! What would:
3 + (-2) = ?
That’s right: 1.
I’ll run through 3 + (-2) with each approach:
Option One - Intuitive Approach: You have 3 dollars in your pocket, and you spend 2 dollars. What do you have left? 1 dollar - don’t spend it all in one place.
Option Two - Rewrite with Subtraction: Adding a negative number is the same as subtracting a positive number.
3 + (-2)
Can be rewritten as:
3 - 2
3 - 2 = 1
Option Three - Number line: Start at the first number, then either hop right for positive numbers or left for negative numbers.
3 + (-2)
Start at 3 on the number line
Make 2 hops to the LEFT.
After 2 hops to the left (2 green dashed arcs) you land at 1
Which option do you prefer to use? Let me know in the comments!