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Lesson 2: Adding negative numbers fluently

Review the basic of adding negative numbers and try some practice problems.

## Adding negative numbers with a number line

Lets add $-6+\left(-7\right)$.
Step 1: Start at the first number, in this case $-6$:
Step 2: Move $7$ more places to the left. We move $7$ to the left because adding negative $7$ decreases our number by $7$.
$-6+\left(-7\right)$ takes us to $-13$ on the number line.
$-6+\left(-7\right)=-13$

### Adding a negative number and a positive number

Lets add $-8+3$.
Step 1: Start at the first number, in this case $-8$:
Step 2: Move $3$ places to the right. We move $3$ to the right because adding positive $3$ increases our number by $3$.
$-8+3$ takes us to $-5$ on the number line.
$-8+3=-5$

## Practice

Problem 1
$5+\left(-4\right)=$

Want to try some more adding negative numbers problems? Check out this exercise.

## Want to join the conversation?

• how do u add 2 negative numbers if 2 negative numbers are positive
• you put a parenthesis on one of the negative numbers
• how will negative numbers help us when we get older
• If your are in debt i guess
• Why is it that when adding two negative numbers they do not equal a positive?
• it is negative because negative = minus; the expression two negatives make a positive is for multiplication, because a negative number times a negative number = a positive one, or when two mines signs are next to each other, then that means a plus sign
• is 0 a prime or composite?
• It it neither. maybe it is composite because 0+0=0
• Why is -4+8= positive 4?
• Picture you have a number chart ranging from -10 to 10. You have a point that sits on -4. Then you move up from -4, 8 times.

-4 (Starting point),-3 (One time),-2 (Two times),-1 (Three times),0 (Four times),1 (Five times),2 (Six times), 3(Seven times) , 4 (Eight Times)

Thus -4+8=4, or you could look at it as 8-4=4.
• I was taught a rhyme when I was learning this I would like to share it hopefully this will help anyone struggling.
It goes like…

Different sign subtract
Keep the sign at the higher value
Then you’ll be exact!

I hope this helps anyone ! :)
• If your going backwards on a number line, then how come you are adding integers sometimes?
• Good question! When we "add" negative numbers to one another, we move further left on the number line. So, -5 + (-2) = -7. I started at -5 and moved another -2, ending up at -7. The operation was "addition" of two negative numbers. (The words we use in math to explain processes can sometimes be confusing. I use the number line all the time to try and understand how to solve the problems like this. Once you get used to seeing how numbers move on the number line it will seem really natural.) Sal's videos are great for explaining this, but do all the exercises and use the hints if you need to. They really help explain this process. Hope this helps!
• When your solving an equation,like: 6(3 + -7) can I just go and start solving the equation and determine if it's a positive or a negative, or do I have to do the number lines?
• You don't really need to have to do the number lines, you can do it any way you want. the answer for equation 6(3+-7) is -24 because you have to share the 6 in 3 and -7 so it is 18+ -42 and that equals -24.
• how do you take the square root of negative number?