### What are negative numbers?

A negative number is any type of number that is much less than zero. For instance, -7 is a number that is salso less than 0.

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-7

It could seem a little odd to say that a number is less than 0. After all, we frequently think of zero as definition nothing. For circumstances, if you have actually 0 pieces of cocoa left in your candy bowl, you have actually no candy. There's nothing left. It's hard to imagine having actually less than nopoint in this case.

However before, there are instances in actual life wright here you usage numbers that are much less than zero. For example, have you ever been external on a really cold winter day as soon as the temperature was below zero? Any temperature listed below zero is an adverse number. For circumstances, the temperature on this thermometer is -20, or twenty degrees below zero.

You can also usage negative numbers for more abstract ideas. For instance, in finances negative numbers can be supplied to display debt. If I overattract my account (take out more money than I actually have), my new financial institution balance will be a negative number. Not just will certainly I have no money in the bank—I'll actually have less than none because I owe the financial institution money.

Watch the video below to learn even more about negative numbers.

Any number without a minus sign in front of it is thought about to be a positive number, definition a number that's greater than zero. So while -7 is negative seven, 7 is positive seven, or ssuggest seven.

Understanding negative numbers

As you might have noticed, you create negative numbers with the exact same symbol you usage in subtraction: the minus sign ( - ). The minus sign doesn't mean you need to think of a number favor -4 as subtract four. After all, exactly how would certainly you subtract this?

-4

You couldn't—because there's nothing to subtract it from. We deserve to write -4 on its very own specifically bereason it doesn't mean subtract 4. It means the opposite of four.

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

You have the right to think of a number line as having actually 3 parts: a positive direction, a negative direction, and zero. Everything to the appropriate of zero is positive and also whatever to the left of zero is negative. We think of positive and also negative numbers as being opposites because they are on opposite sides of the number line.

Anvarious other necessary point to recognize around negative numbers is that they get smaller the farther they get from 0. On this number line, the farther left a number is, the smaller it is. So 1 is smaller than 3. -2 is smaller sized than 1, and also -7 is smaller than -2.

Understanding absolute value

When we talk around the absolute value of a number, we are talking about that number's distance from 0 on the number line. Remember exactly how we shelp 4 and also -4 were the same distance from 0? That suggests 4 and also -4 have actually the exact same absolute worth. We represent taking the absolute value of a number via 2 directly vertical lines | |. For example, |-3| = 3. This is check out "the absolute worth of negative 3 is three."

Something vital to remember: also though negative numbers acquire smaller as they obtain further from 0, their absolute value gets bigger. For instance, -10 is smaller than -6. However before, |-10| is bigger than |-6| because -10 has actually a higher distance from 0 than -6.

### Calculating via negative numbers

Using negative numbers in arithmetic is sensibly basic. There are simply a couple of one-of-a-kind rules to save in mind.

### Adding and subtracting negative numbers

When you're adding and also subtracting negative numbers, it helps to think about a number line, at least at first. Let's take a look at this problem: 6 - 7. Even though 7 is bigger than 6, you deserve to subtract it in the exact exact same way as any other number, as lengthy as you understand also there are numbers smaller than 0.

6 - 7 = -1

While the number line makes it easy to image this trouble, there's additionally a trick you might have offered to settle it.

First, neglect the negative indications for a moment. Just uncover the difference between the 2 numbers. In this instance, it implies resolving for 7 - 6, which is 1. Next, look at your original problem. Which number has the highest possible absolute value? In this situation, it's -7. Because -7 is a negative number, our answer will certainly be one too: -1. Because the absolute value of -7 is greater than the distance between 6 and also 0, our answer ends up being less than 0.

How would you resolve this problem?

6 + -7

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

This is because the plus authorize sindicate lets you understand you're combining two numbers. When you combine an adverse number with a positive one, the amount will be less than the original number—so you might too be subtracting. So 6 + -7 is the very same point as 6 - 7, and they both equal -1.

6 + -7 = -1

Whenever before you watch a positive and negative authorize next to each various other, you must review it as a negative. Similar to 6 + -7 is the very same as 6 - 7:

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

This is true whenever you're including a negative number. Adding an unfavorable number is always the same as subtracting that number's absolute value.

Subtracting negative numbers

If including an adverse number is actually equal to subtracting, how do you subtract an unfavorable number? For instance, just how execute you solve this problem?

6 - - 3

If you guessed that you add them, you're best. Here's why: Remember exactly how we sassist a negative number was the oppowebsite of a positive one? We compared them to you and also your mirror image. Your mirror photo is your oppowebsite, which implies your mirror image's opposite is you. In other words, the oppowebsite of your opposite is you.

In the very same way, you have the right to simplify these two minus signs by analysis them as 2 negatives. The initially minus sign negates—or provides negative—the second. Because the negative—or opposite—of a negative is a positive, you can replace both minus signs with a plus authorize. This indicates you'd fix for this:

6 + 3

This is a lot easier, to deal with, right? If it appears confusing, you deserve to just remember this straightforward trick: When you see two minus signs ago to back, relocation them through a plus sign.

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

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Remembering all of the rules for including and also subtracting numbers can be overwhelming. Watch the video below for a trick to help you.