How Do You Know Which Negative Number Is Greater
Lesson 3: Negative Numbers
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What are negative numbers?
A negative number is any number that is less than zip. For instance, -7 is a number that is seven less than 0.
-seven
It might seem a little odd to say that a number is less than 0. After all, we oft remember of zero as meaning nothing. For example, if you have 0 pieces of chocolate left in your candy bowl, y'all have no candy. There'south nil left. It's difficult to imagine having less than nothing in this case.
However, at that place are instances in existent life where yous use numbers that are less than zero. For case, have you ever been exterior on a really cold winter twenty-four hour period when the temperature was below zippo? Whatever temperature below zero is a negative number. For instance, the temperature on this thermometer is -xx, or twenty degrees below zero.
Y'all can also use negative numbers for more abstract ideas. For example, in finances negative numbers can be used to show debt. If I overdraw my account (take out more than coin than I actually have), my new banking concern balance will be a negative number. Not merely will I have no coin in the depository financial institution—I'll actually accept less than none considering I owe the bank coin.
Sentinel the video below to learn more about negative numbers.
Any number without a minus sign in front of it is considered to be a positive number, meaning a number that's greater than null. Then while -7 is negative seven, vii is positive seven, or simply seven.
Understanding negative numbers
As you might have noticed, yous write negative numbers with the same symbol y'all use in subtraction: the minus sign ( - ). The minus sign doesn't mean yous should think of a number similar -4 as decrease 4. After all, how would you subtract this?
-4
Y'all couldn't—because in that location'south nothing to subtract information technology from. We tin can write -4 on its own precisely because it doesn't mean subtract 4. Information technology means the opposite of four.
Take a await at 4 and -4 on the number line:
Yous tin can recall of a number line equally having three parts: a positive management, a negative management, and zero. Everything to the correct of zero is positive and everything to the left of zero is negative. Nosotros think of positive and negative numbers as being opposites because they are on contrary sides of the number line.
Another important thing to know virtually 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. And so 1 is smaller than three. -2 is smaller than 1, and -7 is smaller than -two.
Understanding absolute value
When we talk about the absolute value of a number, we are talking near that number's distance from 0 on the number line. Remember how we said 4 and -four were the same distance from 0? That means 4 and -4 take the aforementioned absolute value. We represent taking the absolute value of a number with two direct vertical lines | | . For instance, |-3| = 3. This is read "the accented value of negative three is iii."
Something of import to remember: fifty-fifty though negative numbers get smaller equally they get further from 0, their absolute value gets bigger. For example, -10 is smaller than -6. However, |-10| is bigger than |-6| because -ten has a greater distance from 0 than -half-dozen.
Calculating with negative numbers
Using negative numbers in arithmetic is fairly unproblematic. In that location are only a few special rules to proceed in mind.
Adding and subtracting negative numbers
When y'all're adding and subtracting negative numbers, it helps to think about a number line, at least at first. Allow's take a expect at this problem: half-dozen - seven. Even though vii is larger than half dozen, y'all can decrease it in the exact aforementioned mode as whatsoever other number, as long as y'all understand in that location are numbers smaller than 0.
vi - seven = -1
While the number line makes it easy to movie this problem, there's too a trick you could have used to solve it.
First, ignore the negative signs for a moment. Just observe the difference between the two numbers. In this case, it means solving for 7 - vi, which is i. Next, look at your original problem. Which number has the highest absolute value? In this case, it's -7. Because -7 is a negative number, our answer will be ane also: -1. Considering the absolute value of -7 is greater than the distance betwixt 6 and 0, our reply ends upwardly being less than 0.
Adding negative numbers
How would you solve this trouble?
half-dozen + -7
Believe it or not, this is the exact same problem we simply solved!
This is because the plus sign just lets y'all know you're combining two numbers. When yous combine a negative number with a positive i, the sum will be less than the original number—so you might as well exist subtracting. So 6 + -7 is the aforementioned thing as 6 - 7, and they both equal -1.
6 + -vii = -1
Whenever you see a positive and negative sign next to each other, y'all should read information technology every bit a negative. Only similar 6 + -7 is the same as 6 - vii:
- 10 + -eleven is equal to 10 - 11.
- 3 + -ii is equal to 3 - 2.
- 50 + -100 is equal to 50 -100.
This is true whenever you're adding a negative number. Adding a negative number is ever the same as subtracting that number'south absolute value.
Subtracting negative numbers
If calculation a negative number is really equal to subtracting, how do you subtract a negative number? For example, how practice you solve this problem?
half-dozen - - 3
If you guessed that y'all add them, you're right. Here's why: Remember how we said a negative number was the reverse of a positive one? Nosotros compared them to you and your mirror epitome. Your mirror image is your contrary, which means your mirror prototype's contrary is you. In other words, the opposite of your opposite is you.
In the same way, you can simplify these two minus signs by reading them equally two negatives. The offset minus sign negates—or makes negative—the second. Because the negative—or contrary—of a negative is a positive, you tin can replace both minus signs with a plus sign. This means you'd solve for this:
6 + 3
This is a lot easier, to solve, right? If it seems disruptive, yous tin just call up this simple trick: When you see two minus signs dorsum to back , replace them with a plus sign.
So 6 minus negative three is equal to vi plus 3. That's equal to 9. In other words, 6 - -3 is 9.
Remembering all of the rules for adding and subtracting numbers can be overwhelming. Picket the video below for a fox to assistance you.
Multiplying and dividing negative numbers
There are 2 rules for multiplying and dividing numbers:
- If you're multiplying or dividing two numbers that are either both positive or both negative, your result will be positive.
- If y'all're multiplying or dividing a positive number and a negative number, your outcome volition be negative.
That's information technology! You multiply or divide as normal, then use these rules to make up one's mind whether the respond is positive or negative. For instance, take this problem, -three ⋅ -4 . 3 ⋅ iv is 12. Considering both numbers nosotros multiplied were negative, the respond is positive: 12.
-3 ⋅ -4 = 12
On the other hand, if nosotros were to multiply iii ⋅ -4, nosotros'd go a dissimilar answer:
3 ⋅ -4 = -12
Again, three ⋅ 4 is 12. Just because one of our multiples is negative and the other is positive, our answer must too exist negative: -12.
It works the same mode for division. -40 / -10 is 4 because -40 and -10 are both negatives. However, -40 / ten is -4 because ane number is negative and the other is positive.
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Source: https://edu.gcfglobal.org/en/algebra-topics/negative-numbers/1/