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### Course: Arithmetic > Unit 18

Lesson 1: Intro to negative numbers# Intro to negative numbers

Learn what negative numbers are and how to plot them on the number line.

Here's a number line that should look very familiar. It starts at $0$ , then counts up by $1$ from there:

We know that if we were to keep going to the right, we would have $11$ , then $12$ , and so on.

What happens if we keep going to the left of $0$ though? We get negative numbers! To the left of $0$ is $-1$ , then $-2$ , then $-3$ , and so on:

## Let's practice!

## Why do we need negative numbers?

Negative numbers help us describe values less than zero.

### Example:

When the temperature is ${8}^{\circ}$ below ${0}^{\circ}$ , it is less than $0$ . We can say the temperature is $-{8}^{\circ}$ .

### A few more negative situations

## Want to join the conversation?

- can negative numbers become decimals??(147 votes)
**Yes**!

For example:

`-5 = -5.0`

or

`-5.0 = -5`

So

`-5/2 = -2.5`

*and so on....*(168 votes)

- Why do two Negatives equal a positive. Why can't a Negative plus a Negative equal a Negative? Is it just a math rule or is just the way it goes?. For example

"-2+(-3)=?". Thank you, that is my question.(40 votes)- Two negatives equal a positive when you are multiplying or dividing. A negative plus a negative does equal a negative. You are moving down on the number line, so you are getting to smaller numbers.(-2+(-3))is the same as (-2-3). This equals (-5).(49 votes)

- if math is so important then why do people hate math?(21 votes)
- Eating healthy is important, but some people hate vegetables. People generally don't like necessary things that don't give them immediate pleasure in exchange for long-term benefits. Math is one of these. When you work problems, you have to put in effort for no immediate return. However, you gain a better understanding of the world through math, and math can help you with various problems once you've put in the work to know the concept.(86 votes)

- can negative numbers become fractions?(28 votes)
- Absolutely, if the problem is such that a fraction will be formed. The negative sign does not affect whether a number will be a fraction or not.(54 votes)

- Can negative numders be turned into a fraction,decimal,and percent? If yes how can you do that?(27 votes)
- Yes, they can. The negative sign doesn't do anything special. Just pretend it doesn't exist, and continue on with the calculation.

For example, -1.6 = -8/5 because 1.6 = 8/5.(38 votes)

- can negative numbers be decimals(12 votes)
- I'm Sad :( i don't understand subtraction... for the negative(15 votes)
- There is 2 scenarios of subtraction for the negative, when subtract positive number from negative number and when you subtract negative number from negative number, shortly:

1. -a-b (or -a-(+b) 'b' is positive number but + sign is usually omitted)

2. -a-(-b)

It is always handy to imagine '-a' as a point on a number line not just something from wonderland it's just a point on a numberline just as any other integer.

Tricky things start with 'b'. I suggest thinking about it like this, positive numbers they are like honest dear people, they always act as they are expected to act when they are used to subtract from number (doesn't matter if it is negative or positive) they make number (in our case 'a') less than it was before subtraction same thing with addition they always make number bigger than it was.Negative numbers are like cunning and deceiving people they always do opposite of what they are expected to do when you subtract negative number they suddenly make number bigger than it was, same thing with addition they make number less then it was.

Also it is helpful to always keep in mind that the farther from zero a negative number is, the smaller it gets, even though the integer is getting bigger because as I said negative numbers are like deceiving people they always act opposite of what they are look like

P.S. In formula -a-(-b) ain't -(- looks like + sign it may help because

-a-(-b) and -a+b is the same thing(12 votes)

- so if you with drawl $100,000 from the bank the bank will cont that as -100,000 but its adding to you.(12 votes)
- Yes.But you would have to pay back later.(15 votes)

- can you have a variable be a negative number?(12 votes)
- Yes, you can! A variable can be pretty much anything, negative numbers and decimals included. Hope I helped, have a nice day :)(10 votes)

- can there be a number to a negative power?(7 votes)
- Great question for 6th grade!

The answer is yes! A negative sign in the exponent means taking the reciprocal in the answer.

Example: 4^(-3) = 1/(4^3) = 1/(4 * 4 * 4) = 1/64.

Have a blessed, wonderful day!(20 votes)