You can put this solution on YOUR website!
the problem is:
you solve the expression within the inner set of parentheses first.
there is no set of inner parentheses here, so you solve the expression within the leftmost set of parentheses first and then solve the expression within the right set of parentheses next.
the expression within the first set of parentheses is:
working from left to right, you perform multiplies and divides first and then go back and do pluses and minuses.
this expression becomes:
(1/2) + (1/3)
since the division has already been simplified as far as it can go, you then do pluses and minuses.
in this case, you need to get a common denominator.
the common denominator is 6, so you multiply 1/2 by 3/3 and you multiply 1/3 by 2/2 to get:
(3/6) + (2/6) which you can now combine to become equal to:
you resolve the next set of parentheses next.
that set is:
(2/3 - 1/12)
since your multiplies and divides have been simplified as far as they can go, you then do your pluses and minuses.
you need to get a common denominator.
the smallest common denominator is 12.
you multiply 2/3 by 4/4 and you multiply 1/12 by (1/1) which means you don't have to multiply 1/12 by anything to get a denominator of 12 because it already has one.
(8/12 - 1/12) which becomes:
you are left with:
(5/6) / (7/12) which is the same as:
(5/6) * (12/7) which is the same as:
(5*12) / (6*7) which becomes:
60 / 42 which can be simplified to:
in your scientific calculator, you would enter your expression as follows:
the calculator should give you an answer of 1.428571429
multiply this answer by 7 and you will get an answer of 10.
1.428571429 is equivalent to 10/7.
the order of operations is:
powers and roots first scanning from left to right.
multiplies and divides next scanning from left to right.
adds and subtracts next scanning from left to right.
you repeat these steps within each set of parentheses working from the innermost set of parentheses first and then proceeding to the outer-most set of parentheses.
you might think that 1/2 hasn't been resolved as far as it will go and you would be correct.
1/2 is equal to .5
once you get .5 you have resolved the division as far as it will go.
you can, however, leave it in fraction form as we did above and assume it's been resolved as far as it will go because there's no other operation other than simplification that might be needed to reduced it even further.
working with fractions is where the waters get muddy and you simply have to know and understand whether or not you need to work the operation any further.
in your problem, if i took a strict definition, i would have done the following:
(1/2+1/3)/(2/3-1/12) simplifies to:
(.5 + .333333333) / (.666666667 - .0833333333)
lots of endless fractional parts in this expression but the calculator can handle them well if you save the intermediate results into memory.
this now becomes:
.83333333333 / .583333333333
1.428571429 which is the decimal equivalent of 10/7.