What are an unfavorable numbers?

A negative number is any number the is much less than zero. Because that instance, -7 is a number the is seven less 보다 0.

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

However, there space instances in real life where you use numbers that are less than zero. For example, have actually you ever been external on a really cold winter day when the temperature was below zero? any kind of temperature below zero is a an unfavorable number. Because that instance, the temperature ~ above this thermometer is -20, or twenty degrees below zero.


You can additionally use negative numbers for more abstract ideas. Because that instance, in finances an unfavorable numbers have the right to be offered to display debt. If i overdraw my account (take out more money 보다 I in reality have), my brand-new bank balance will be a negative number. Not just will I have actually no money in the bank—I'll actually have actually less 보다 none because I owe the financial institution money.

Watch the video below come learn an ext about an adverse numbers.

Any number without a minus sign in prior of that is thought about 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 just seven.

Understanding negative numbers

As you can have noticed, girlfriend write negative numbers with the same symbol you use in subtraction: the minus sign ( - ). The minus authorize doesn't typical you need to think the a number favor -4 as subtract four. After all, just how would girlfriend subtract this?


You couldn't—because there's nothing come subtract the from. We deserve to write -4 on its own precisely since it doesn't average subtract 4. It method the opposite that four.

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


You deserve to think that a number line as having actually three parts: a positive direction, a negative direction, and also zero. Whatever to the best of zero is positive and everything to the left of zero is negative. We think of confident and negative numbers together being opposites because they space on opposite sides of the number line.

Another crucial thing to understand about an adverse numbers is the they gain smaller the furthermore they obtain from 0. Top top this number line, the farther left a number is, the smaller it is. Therefore 1 is smaller sized than 3. -2 is smaller than 1, and -7 is smaller sized than -2.


Understanding absolute value

When us talk around the pure value the a number, we room talking about that number's street from 0 on the number line. Remember how we claimed 4 and -4 were the same distance from 0? That means 4 and -4 have actually the exact same absolute value. We stand for taking the absolute value of a number v two right vertical present | |. For example, |-3| = 3. This is read "the absolute worth of negative three is three."


Something necessary to remember: even though an unfavorable numbers get smaller together they get more from 0, your absolute worth gets bigger. For example, -10 is smaller than -6. However, |-10| is bigger than |-6| because -10 has a higher distance indigenous 0 보다 -6.

Calculating with negative numbers

Using an unfavorable numbers in arithmetic is reasonably simple. There are just a couple of special rules to store in mind.

Adding and subtracting negative numbers

When you're adding and subtracting an unfavorable numbers, it help to think about a number line, at the very least at first. Let's take a look at this problem: 6 - 7. Even though 7 is bigger than 6, you deserve to subtract the in the exact same method as any type of other number, as long as you know there space numbers smaller 보다 0.


6 - 7 = -1

While the number line provides it easy to photo this problem, there's also a trick you might have provided to deal with it.

First, ignore the negative signs for a moment. Just find the difference between the two numbers. In this case, it way solving because that 7 - 6, i beg your pardon is 1. Next, look at your initial problem. I beg your pardon number has actually the highest absolute value? In this case, it's -7. Since -7 is a negative number, our answer will be one too: -1. Since the absolute worth of -7 is higher than the distance in between 6 and also 0, ours answer ends up gift less 보다 0.

Adding an unfavorable numbers

How would certainly you fix this problem?

6 + -7

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

This is because the plus authorize simply allows you know you're combining two numbers. Once you incorporate a an unfavorable number v a optimistic one, the amount will it is in less 보다 the original number—so you might also be subtracting. Therefore 6 + -7 is the very same thing as 6 - 7, and they both same -1.

6 + -7 = -1

Whenever you watch a hopeful and negative sign alongside each other, you need to read it as a negative. Similar to 6 + -7 is the very same as 6 - 7:

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

This is true anytime you're adding a an unfavorable number. Including a negative number is always the same as subtracting the number's pure value.

Subtracting an unfavorable numbers

If including a negative number is in reality equal to subtracting, just how do you subtract a negative number? for example, just how do you solve this problem?

6 - - 3

If friend guessed the you add them, you're right. Here's why: Remember just how we claimed a an adverse number to be the opposite of a positive one? We contrasted them to you and your winter image. Her mirror photo is her opposite, which method your mirror image's opposite is you. In various other words, opposing of her opposite is you.

In the very same way, you can simplify these 2 minus indications by reading them as 2 negatives. The very first minus authorize negates—or makes negative—the second. Since the negative—or opposite—of a negative is a positive, you can replace both minus indicators with a add to sign. This method you'd deal with for this:

6 + 3

This is a lot easier, come solve, right? If it seems confusing, you can just remember this basic trick: When friend see two minus signs back to back, change them with a to add sign.

So 6 minus negative 3 is same 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 individually numbers can be overwhelming. Clock the video clip below because that a cheat to help you.