### 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**.

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**.

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 numbersIf 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.