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Lesson 6: Adding & subtracting negative numbers: variables

# Substitution with negative numbers

Practice substituting positive and negative values for variables.

## Want to join the conversation?

• evaluate 1+ (-2/3)- (-m) where m = 9/2
I got 30/6 or 5 but the answer is 29/6...I am lost to how...
• Hey zkbaby311. I know this is a little late to answer your question but I hope it helps. This problem was a little difficult for me too, but when I finally figured out how to do it correctly, it was no big deal.

Step 1: You have to add 1 and -2/3 together. You will get 1/3 as an answer.
Step 2: Then, since we know 9/2 is the variable m we have to add 1/3 to 9/2. The reason we add both fractions is because there are two minus signs that indicate we are adding.
Step 3: This is the tricky part here. Since both fractions have different denominators, we have to change them to a common denominator. I changed 9/2 into 27/6 and 1/3 to 2/6. This will work because 27+2=29! So your final answer will be 29/6!
• I would be so helpful if you could restart the unit test.
Instead of needing to fully complete it.
• That would be nice because we all make silly mistakes sometimes even when we know what we are doing.
• At how it is 12. The equation is supposed to be 5-(- -7). The answer is supposed to be -2.
• no. It's supposed to be 5-(-7), in which the minus symbol and the negative symbol cancel out each other, making the equation then 5+7, equalling 12.
• I still don't understand how to do the equations.
• Let me help Laura! okay so whenever you see -(- just connect them and you get... + and the numbers become positive except if there is a negative in the front. So let's try it!
-5-(-8)= -5+8=3

Now if you have +(- you just add (if both are negitive numbers) or subtrcat (if one nuber positive and other negitive). Lets try it!
5+(-9)=5-9=-4

Hope this helps!
• I'm actually still quite confused, for the second problem, I got -2 as my answer but the person in the video got 12 so I'm still a little confused on that.
• Let's work this out, step by step.

Here's our original expression:
3 - (-6) + (-h) + (-4)
We also know that h = -7, so let's substitute that into the expression:
3 - (-6) + (-(-7)) + (-4)
(-(-7)) evaluates to positive 7. The two negative signs "cancel" each other out, therefore producing a positive outcome. You can think of this as the opposite of the opposite of 7, which is still positive 7.
3 - (-6) + 7 + (-4)
As for -(-6), it is similar to (-(-7)). You are taking the opposite of -6, which is positive 6.
3 + 6 + 7 + (-4)
+(-4) evaluates to -4.
3 + 6 + 7 - 4
Now we can follow the Order of Operations and solve the expression. The Order of Operations dictates that when we face both addition and subtraction in an expression, we evaluate them from left to right. Therefore:
3 + 6 + 7 -4
9 + 7 - 4
16 - 4
12
Therefore, that is how the Sal got 12 in the video. I know this is not the way Sal solved it, but perhaps this method makes more sense to you. Please feel free to comment if you have any more questions.
• How come the questions you get are easier than the questions I get?
• i dont understand this at all
• That's ok!
Here are some basics you may know or not know.

1 - -4 -- (pretend that flips into a +)
1 + 4
5
Therefore, 1 -(-4) = 5.

5 + -3 =
Well, adding a negative is basically subtraction.
5 - 3
2

There are other things that I don't have time to add. But I hope this helped!
• why does -(-10)=10?
• -(-10)=10 because basically you're multiplying -1 to -10. And you know from negative number multiplication that if you multiply the same symbols twice you get a positive number.
• help! im not getting the same answer as sal. i did it in the previous order that the question was, and i keep on getting -2
but when u change the order like he did, i get the same answer as him.! how come?
• Oh, I think I found your error. Changing the order is fine, but you substituted incorrectly. Putting (-h) where h = -7 would give (-(-7)), which is positive (7). Now you should get 12.

I'll do the steps for the different order.

3 - (-6) + (-h) + (-4) =
SUBSTITUTE FOR h:
3 - (-6) + (-(-7)) + (-4) =
3 + 6 + 7 - 4 =
16 - 4 =
12.

Hope this helped :D

9 - h - 4 =
9 - (-7) - 4 =
9 + 7 - 4 =
16 - 4 =
12
• If you have any problems with the subtracting or adding or anything here is a little guide:
Situation 1:
1 -(-1) would be equal positive 2
it would be the same as
1 + 1 because the two negatives cancel each other out and make a positive, aka (+).
Situation 2:
-2 + (-10) would be equal to negative 12 aka (-12).
this is because when you add a negative number to a negative number, think of just like 2 + 10, 12, then just make it negative and that will be your answer.
Situation 3:
-2 + 10, this would equate to positive 8, when you are adding a negative number to a positive, and the positive is greater than the negative, you know the answer will be positive, furthermore think of it as 10 - 2. but if the negative is greater than the positive, such as 2 + (-10), the answer will always be negative, or (-8)

Hope this helped and have a great day!
:)