What are an adverse numbers?

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

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It might seem a small odd come say that a number is less than 0. ~ all, we regularly think of zero as definition nothing. Because that instance, if you have actually 0 pieces of cacao left in your 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 actual life where you usage numbers that are much less than zero. Because that example, have actually you ever been outside on a really cold winter day as soon as the temperature was below zero? any kind of temperature listed below zero is a an adverse number. For instance, the temperature ~ above this thermometer is -20, or twenty levels below zero.


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

Watch the video clip below to learn an ext about an adverse numbers.

Any number without a minus sign in former of that is thought about to it is in a positive number, definition 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 could have noticed, you write an adverse numbers through the exact same symbol you usage in subtraction: the minus sign ( - ). The minus sign doesn't typical you must think that a number favor -4 as subtract four. After ~ all, exactly how would girlfriend subtract this?


You couldn't—because there's nothing come subtract the from. We deserve to write -4 top top its very own precisely because it doesn't median subtract 4. It method the opposite of four.

Take a look in ~ 4 and also -4 top top the number line:


You deserve to think the a number heat as having 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 the zero is negative. Us think of confident and an unfavorable numbers as being opposites because they are on opposite political parties of the number line.

Another essential thing to know about negative numbers is the they gain smaller the farther they gain from 0. ~ above this number line, the aside from that 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 about the absolute value of a number, we space talking around that number's distance from 0 top top the number line. Remember just how we claimed 4 and also -4 were the very same distance native 0? That way 4 and also -4 have the very same absolute value. We represent taking the absolute worth of a number v two right vertical currently | |. For example, |-3| = 3. This is check out \"the absolute value of an unfavorable three is three.\"


Something necessary to remember: even though an adverse numbers acquire smaller together they get further from 0, their absolute value gets bigger. For example, -10 is smaller sized than -6. However, |-10| is bigger 보다 |-6| since -10 has actually a greater distance native 0 보다 -6.

Calculating with an unfavorable numbers

Using negative numbers in arithmetic is relatively simple. There are simply a couple of special rule to save in mind.

Adding and also subtracting negative numbers

When you're including and subtracting an unfavorable numbers, it helps to think about a number line, at the very least at first. Let's take it a look in ~ this problem: 6 - 7. Even though 7 is larger than 6, you have the right to subtract the in the precise same way as any other number, as lengthy as you know there space numbers smaller 보다 0.


6 - 7 = -1

While the number line provides it simple to picture this problem, there's likewise a trick you could have provided to settle it.

First, neglect the negative signs for a moment. Just find the difference in between the two numbers. In this case, it method solving because that 7 - 6, which 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. Due to the fact that -7 is a an adverse number, our answer will certainly be one too: -1. Since the absolute value of -7 is greater than the distance between 6 and 0, ours answer ends up gift less than 0.

Adding an adverse numbers

How would you deal with this problem?

6 + -7

Believe that or not, this is the precise same trouble we just solved!

This is since the plus authorize simply lets you know you're combining two numbers. As soon as you combine a an unfavorable number through a confident one, the amount will it is in less than the original number—so girlfriend might too be subtracting. So 6 + -7 is the very same thing together 6 - 7, and also they both same -1.

6 + -7 = -1

Whenever you check out a optimistic and an adverse sign alongside each other, you need to read it together a negative. Just like 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 including a negative number. Including a negative number is constantly the same as subtracting that number's absolute value.

Subtracting an adverse numbers

If including a an adverse number is in reality equal come subtracting, how do you subtract a an adverse number? for example, how do you solve this problem?

6 - - 3

If you guessed that you add them, you're right. Here's why: Remember how we claimed a an adverse number was the the contrary of a positive one? We compared them come you and also your mirror image. Your mirror photo is your opposite, which means your winter image's the contrary is you. In various other words, opposing of her opposite is you.

In the very same way, you have the right to simplify these 2 minus indicators by analysis them as 2 negatives. The very first minus authorize negates—or makes negative—the second. Due to the fact that the negative—or opposite—of a an unfavorable is a positive, you deserve to replace both minus indications with a to add sign. This way you'd deal with for this:

6 + 3

This is a lot of easier, to solve, right? If it appears confusing, you deserve to just psychic this simple trick: When girlfriend see two minus signs back to back, replace them v a to add sign.

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

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