Order of operations and variables

[tcondon]

best strategy to explain how to solve the following problem:

12^2 / 4b + 4 when b=9

Some students evaluated teh problem and got 8 while others got 338.

[Mr. Hui]

Corrected. Thank you jcsites and MAS1.



Substitute the value of 9 for b:


Evaluate exponents:


Divide:


Multiply:


Add:

Pemdas

12 ^ 2 / 4 * 9 + 4
144 / 4 * 9 + 4
36 * 9 + 4
324 + 4
328

[jcsites]

Originally Posted by tcondon

best strategy to explain how to solve the following problem:

12^2 / 4b + 4 when b=9

Some students evaluated teh problem and got 8 while others got 338.

It should be 328. The precedence of operation is as follows: exponentiation, division, multiplication and addition. Some got 8 because they first multiplied 4 with 9. However, since division and multiplication are of the same precedence, division is evaluated first.

[tcondon]

Edit: Please check the correction in post #2

That is the rule that states you do 4b before dividing 144/4? Anything about solving teh variable expressions first. Even the responses on this question are not the same. I appreciate any feedback.

[Mr. Hui]

Edit: Please check the correction in post #2

[MAS1]

Originally Posted by Mr. Hui

You can do 144/4 or 4b first. The order does not change the answer.

I think this a case where a pair of parentheses can clear up a lot of confusion.

Mr. Hui is assuming that the above expression, as written, is equivalent to:

12^2 / (4b) + 4 so that when b = 9 the answer is 4. When he says it doesn't matter what order you evaluate 144/4 or 4b first he is assuming you would get either 144/4/9, or 144/36 which are the same.

However, others are assuming that the expression is equivalent to:

(12^2 / 4) x b + 4 which evaluates to 328.

As the expression is originally written I believe it has to be evaluated the second way so that the answer is 328.

12^2 / 4b + 4
144 / 4b + 4 Evaluate exponents
36 x b + 4 Evaluate division left to right
36 x 9 + 4 Substitution
324 + 4 Multiplication
328 Addition

The 4b term is what is confusing as we are used to treating it as a term in itself so that it seems like we have 144 / 36 when b = 9.