When Creating a multiple choice problem for a test....

Question

When Creating a multiple choice problem for a test, the person making the test creates incorrect answers to include in the choices. Frequently, these incorrect answers are the ones you might get if you made a common error in solving a problem for example:

9+33÷ 3+4-4 ÷ 2 x 2 =
A. 14
B.23
C.20

Your task is to do both of the following:
1. Choose the corrects answer and show how to get it.
2. Explain the common error that would result in each of the incorrect answer choices.

Please Explain!

Answer 1

If you see a question like this, that looks like straightforward arithmetic, but involves multiplication, division, addition, and subtraction (or any combination of those), you should be thinking "This is probably testing me on Order of Operations."

 

With Order of Operations, remember PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.  This tells you which operations to do before other operations.  If there are more than one of each type (e.g. multiplication AND division) in the problem, do those operations from left to right.

 

For this problem, it might help to group the terms together with parentheses:

 

9+33÷3+4-4÷2x2 could be rewritten

 

9+(33÷3)+4-((4÷2)x2)  This way, you only have to do operations with two numbers at a time.

 

This becomes  9+11+4-(2X2)

Which becomes  9+11+4-4=20

 

The correct answer is C. 20.   

 

If you just did the operations from left to right, you would get  wrong answer A. 14

If you looked at the end of the expression as 4÷(2x2) instead of (4÷2)x2, but did everything else correctly, you'd get wrong answer B. 23