What are an adverse numbers?

A negative number is any type of number that is less than zero. For instance, -7 is a number the is seven less 보다 0.

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It might seem a little odd to say the a number is less than 0. After ~ all, we regularly think of zero as meaning nothing. Because that instance, if you have 0 pieces of coco left in her candy bowl, you have no candy. There's nothing left. It's an overwhelming to imagine having less 보다 nothing in this case.

However, there room instances in real life where you use numbers the are much less than zero. Because that example, have you ever been outside on a yes, really cold winter day once the temperature was listed below zero? any temperature listed below zero is a an adverse number. For instance, the temperature on this thermometer is -20, or twenty levels below zero.


You can additionally use negative numbers for more abstract ideas. For instance, in finances an unfavorable numbers deserve to be used to present debt. If ns overdraw my account (take out an ext money than I actually have), my new bank balance will be a an unfavorable number. Not only will I have no money in the bank—I'll actually have actually less 보다 none because I owe the bank money.

Watch the video below to learn much more about an adverse numbers.

Any number there is no a minus authorize in former of the is taken into consideration to be a positive number, an interpretation a number that's greater than zero. Therefore while -7 is negative seven, 7 is positive seven, or merely seven.

Understanding an unfavorable numbers

As you can have noticed, friend write an adverse numbers with the exact same symbol you use in subtraction: the minus authorize ( - ). The minus authorize doesn't average you must think that a number like -4 together subtract four. After all, just how would you subtract this?


You couldn't—because there's nothing to subtract that from. We have the right to write -4 ~ above its own precisely because it doesn't average subtract 4. It means the opposite that four.

Take a look at 4 and also -4 on the number line:


You deserve to think the a number heat as having actually three parts: a positive direction, a negative direction, and also zero. Every little thing to the best of zero is positive and everything to the left of zero is negative. We think of hopeful and an adverse numbers together being opposites since they space on opposite sides of the number line.

Another necessary thing to know about an unfavorable numbers is the they acquire smaller the aside from that they gain from 0. On this number line, the farther left a number is, the smaller sized it is. So 1 is smaller sized than 3. -2 is smaller than 1, and also -7 is smaller than -2.


Understanding absolute value

When us talk around the absolute value that a number, we space talking about that number's distance from 0 on the number line. Remember how we said 4 and also -4 were the very same distance native 0? That method 4 and -4 have actually the exact same absolute value. We stand for taking the absolute worth of a number with two right vertical lines | |. For example, |-3| = 3. This is check out "the absolute worth of an adverse three is three."


Something necessary to remember: also though an unfavorable numbers get smaller together they get additional from 0, their absolute value gets bigger. Because that example, -10 is smaller sized than -6. However, |-10| is bigger than |-6| due to the fact that -10 has actually a better distance native 0 보다 -6.

Calculating with an adverse numbers

Using negative numbers in arithmetic is fairly simple. Over there are simply a couple of special rule to store in mind.

Adding and subtracting an adverse numbers

When you're adding and subtracting an adverse numbers, it help to think about a number line, at least at first. Let's take a look at this problem: 6 - 7. Also though 7 is larger than 6, you can subtract that in the exact same way as any kind of other number, as lengthy as you know there room numbers smaller than 0.


6 - 7 = -1

While the number line renders it straightforward to picture this problem, there's likewise a trick you might have used to fix it.

First, disregard the an unfavorable signs for a moment. Just discover the difference between the 2 numbers. In this case, it means solving for 7 - 6, i m sorry is 1. Next, look at your original problem. I m sorry number has actually the highest pure value? In this case, it's -7. Because -7 is a an unfavorable number, ours answer will be one too: -1. Because the absolute value of -7 is higher than the distance between 6 and 0, ours answer ends up gift less than 0.

Adding an adverse numbers

How would you resolve this problem?

6 + -7

Believe it or not, this is the specific same trouble we just solved!

This is due to the fact that the plus authorize simply lets you know you're combining 2 numbers. When you combine a negative number with a confident one, the amount will it is in less than the initial number—so you might too be subtracting. For this reason 6 + -7 is the very same thing together 6 - 7, and also they both same -1.

6 + -7 = -1

Whenever you view a hopeful and an adverse sign alongside each other, you should read it together a negative. As with 6 + -7 is the exact same as 6 - 7:

10 + -11 is same to 10 - 11.3 + -2 is equal to 3 - 2.50 + -100 is equal to 50 -100.

This is true at any time you're adding a negative number. Including a an unfavorable number is constantly the exact same as subtracting that number's pure value.

Subtracting an unfavorable numbers

If adding a an unfavorable number is actually equal to subtracting, how do you subtract a an unfavorable number? for example, exactly how do you fix this problem?

6 - - 3

If girlfriend guessed that you add them, you're right. Here's why: Remember how we claimed a an adverse number to be the the contrary of a optimistic one? We contrasted them come you and also your mirror image. Your mirror picture is her opposite, which way your mirror image's the contrary is you. In other words, the opposite of her opposite is you.

In the same way, you can simplify these 2 minus indicators by reading them as two negatives. The very first minus sign negates—or renders negative—the second. Because the negative—or opposite—of a an adverse is a positive, you can replace both minus signs with a to add sign. This method you'd settle for this:

6 + 3

This is a lot of easier, come solve, right? If it appears confusing, you can just remember this basic trick: When you see 2 minus signs back to back, replace them through a to add sign.

So 6 minus negative 3 is equal to 6 plus 3. That's same to 9. In other words, 6 - -3 is 9.

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Remembering all of the rules for adding and subtracting numbers have the right to be overwhelming. Watch the video below for a trick to help you.