5-2 Solve Equations Mentally

To find the missing variable you need to do mental math. If you are dealing with an addition problem, subtract the number given with the answer. This will give you the variable. If you are dealing with a subtraction problem you will need to count backwards from the number given to the answer to find the variable.

#1) 3 + d = 11
Since you have an addition problem, you can easily subtract the two numbers. 11 - 3 = 8.
So d = 8

#2) 15 - r = 2
Since you have a subtraction problem, I need you to visualize the number 15. Start counting backwards and put up one finger for each number you say, until you say the number 2. Like this 14 (put up 1 finger), 13 (put up 2 fingers), 12 (put up 3 fingers), 11(put up 4 fingers), 10(put up 5 fingers), 9(put up 6 fingers), 8(put up 7 fingers), 7(put up 8 fingers), 6(put up 9 fingers), 5(put up 10 fingers)....uh-oh, we aren't to 2 yet, remember that we got to 10 ok? And start over with your fingers... 4 (put up 1 finger), 3(put up 2 fingers), 2(put up 3 fingers)...whew! Remember how we already got to 10 fingers then put up 3 more.....10+3 = 13......
So r = 13

But the finger subtraction only works if the missing variable comes second in the equation. What if it comes first? Look at #6

#6) 9 = w - 12
I hate looking at problems with the answer first, so I'll just scoot the =9 to the other side
w - 12 = 9
We cannot use the counting backwards method for this or you'll get a tiny number to put first in a subtraction problem, which we all know is a no-no.
Instead, I want you to add the two numbers given to you. 12+9 = 21
So w=21

So basically:
All addition problems with a missing variable will be solved by subtracting the two numbers given, regardless of the placement of the missing variable.
A subtraction problem with the missing variable first can be solved by adding the two numbers given.
A subtraction problem with the missing variable second can be solved by counting backwards from the given variable to the answer.