eli5 Difference between (5+6) x 3-1 and 5+6 x (3-1)

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According to the calculator they have different answers, the first being 32 and the latter being 17. I got the answer 22 when i worked it out.

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(5+6) x 3 – 1 Is essentially (11 x 3) – 1 = 32
Whereas 5 + 6 x (3 – 1) is 5 + (6 x 2) = 17
Brackets come first, then multiplication

Write **all** the brackets and the difference becomes obvious:

((5 + 6) x 3) – 1
vs
5 + (6 x (3 – 1))

I’ve always been taught PEMDAS, but I’ve heard conflicting explanations on that. So I’ll tell you how I personally got to my answers.

First equation: do parentheses first. So 5+6= 11, then do multiplication. 11×3= 33. Finally subtract the 1. Answer =32.

Second equation: parentheses first. 3-1= 2. Then multiplication. You would have 5+6×2. Or 5+ 6(2) = 5+12 which would be 17.

The difference results in the order of operations.

1st one is 11×3 and then -1

2nd one is 11×2

Rewriting your equations so that left-to-right matches the order of operations:

(5+6)*3 – 1 = 11*3 – 1 = 33 – 1 = 32

(3-1)*6 + 5 = 2*6 + 5 = 12 + 5 = 17

*Always* finish the inside of the brackets/parenthesis first. That’s what they mean; “do this part first before anything else”. If you fail to do that, then you are doing wrong math.