Question 365466: What is the order to follow when working a math problem. For instance 5-3÷3= WHAT
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! For instance 5-3÷3
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The rule calls for two scans.
The 1st is left to right for multiplication and division.
The 2nd is left to right for addition and subtraction.
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Your Problem:
5-3/3
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1st scan results:
5-1
2nd scan results:
4
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Cheers,
Stan H.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the order is:
you work from left to right.
expressions within the inner set of parentheses are done first.
expressions within the outer set of parentheses are done next.
an expression without any parentheses has an implied set of parentheses that surrounds the whole problem.
within each set of parentheses:
radicals and exponents are processed first from left to right.
multiplication and division are processed second from left to right.
addition and subtraction are processed third from left to right.
in your problem, your expression is:
5-3/3
there are no inner parentheses to process first.
an outer set of parentheses is implied which would make your equation look like:
(5-3/3)
you have no radicals or exponents so these do not have to be done.
you have a division so that is done next to get:
( 5 - (3/3) ) = (5 - 1)
you have a subtraction, so you process that next to get:
(5 - 1) = (4)
the outer set of parentheses does not have to be shown, so your answer is 4.
looking back at your original problem, if you inserted parentheses where required, it would have looked like this:
(5 - (3/3)).
the inner set of parentheses would have been processed first to get:
(5 - 1).
the outer set of parentheses would have been processed next to get 4.
the parentheses can alter the order of operations.
in your example, it was implied that:
5 - 3/3 was the same as (5 - (3/3))
to alter the order of operations, you would put the parentheses surrounding the operations you wanted to be performed first.
in this case, if you wanted to subtract the 3 from the 5 before dividing by 3, then you would have had to use parentheses as follows:
((5-3)/3)
now the inner set of parentheses is still done first, but in this case it is the subtraction.
you would get (2/3) which becomes 2/3.
without any parentheses at all, the order of operations is:
exponents and radicals first from left to right.
multiplication and division second from left to right.
addition and subtraction third from left to right.
this is the same order as shown above for within each set of parentheses.
process from left to right means that, if the order of the operations is the same, then you do the leftmost operations before doing the rightmost operations.
5 - 3 / 3 + 7 + 8/4 + 8 + 3^2 would be processed as follows:
3^2 would be processed first to get 9
3/2 would be processed next to get 1
8/4 would be processed next to get 2
your formula would become:
5 - 1 + 7 + 2 + 8 + 9
5-1 would be processed next to get 4
4+7 would be processed next to get 11
11+2 would be processed next to get 13
13 + 8 would be processed next to get 21
21 + 9 would be processed next to get 30.
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