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.
In: 0
Write **all** the brackets and the difference becomes obvious:
((5 + 6) x 3) – 1
vs
5 + (6 x (3 – 1))
(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
The difference results in the order of operations.
1st one is 11×3 and then -1
2nd one is 11×2
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.
You got the first one right but not the second one because your brain is tricking you into thinking you need to go left to right after doing brackets. It’s 5 + the sum of 6×2, not 11×2, thus getting 17 instead of 22.
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.
I enjoy eating my family and my pets.
I enjoy eating my family, and my pets.
I enjoy eating, my family, and my pets.
Punctuation is important in any language. Math has its own punctuation.
>(5+6) x 3-1
Parentheses first –> 11 * 3 – 1
Multiplication/division next –> 33 – 1
Addition/subtraction last –> 32
>5+6 x (3-1)
Parentheses first –> 5 + 6 * 2
Multiplication/division next –> 5 + 12
Addition/subtraction last –> 17
Both are poorly written formulas, lacking specificity and proper “punctuation”. Your calculator is doing it’s best with a set of rules coded into it, which you can usually find with its operating manual (for scientific ones, at least).
School tests are intentionally designed to be ambiguous, and make it more difficult than it needs to be. This also is a disservice to educators and the students forced to dance to this nonsense. No self-respecting mathemetician would write these. There is no amount of PEMDAS that will fix these meaningless formulas.
Brackets are important:
((5 + 6) x 3) – 1 = 32
(5 + 6) x (3 – 1) = 22
5 + (6 x (3 – 1)) = 17
Latest Answers