I have been having problems with this skill testing question. I know the rules of operation but I don't understand why they would put it in brackets. Can you help me. I have two answers but I would like to know which one is right. Im having a disagreement with a friend over this matter. Thank you so much

[ (20 + 82 - 6) ÷ 16 ] x 14

We have two responses to your question.

From Sue:

Hi there.

There is a famous acronym in arithmetic: BEDMAS. It gives the order of operations (what operations to do in proper order).
B = Brackets (or parentheses or braces). Start by working out the values inside the innermost parentheses first.
E = exponents (you don't have any of these)
D, M = division and multiplication
A, S = addition, subtraction are the last things you do.

Other than that, you proceed from left to right.

You are right that in your example, the brackets aren't really affecting how things work out, because the ÷ 16 would happen before the x 14 anyway. The total I get is 84. That's the only correct answer to this expression.

Stephen La Rocque.>

and from Paul:

Hi,

BEDMAS stands for
Brackets, exponents, division, multiplication, addition, subtraction
- this is the order we do calculations: brackets first, then exponents, then division and multiplication in order from left to right, then addition and subtraction in order from left to right.

[ (20 + 82 - 6) ÷ 16 ] x 14
= [ (102 - 6) ÷ 16] x 14
= [ (96) ÷ 16 ] x 14
= [ 96 ÷ 16] x 14
= [ 6 ] x 14
= 6 x 14
= 84

Note - given that we do division and multiplication in order from left to right, the square brackets are not needed:
(20 + 82 - 6) ÷ 16 x 14
= 96 ÷ 16 x 14 (do division first since it comes first moving from left to right)
= 6 x 14
= 84
Perhaps to square brackets are included to "trick" you. But, they are redundant in terms of the rules of order of operations.

We have have to use brackets to do the multiplication first:
(20 + 82 - 6) ÷ (16 x 14)
= (96) ÷ (224)
= 96 ÷ 224
= 0.428571428571...

Paul