What is the value of (1/2-1/6) ÷2/3+1/4?
(1/2–1/6) / (2/3+1/4)
I assume that’s the exact format you meant to write.
first, convert all terms in each set of parentheses to like terms with each other.
(1/2 - 1/6) / (2/3 + 1/4)
(3/6–1/6) / (8/12+3/12)
(2/6)/(11/12)
Multiply the result by the inverse of the denominator; it has the same net effect as dividing it. This changes the expression to:
(2/6) * (12/11)
24/66
Reduce, with a GCF of 2:
12/33
If you’re confused by my logic then consider the following expression:
30 / 3/5
Convert the 3/5 to a decimal and you get:
30/0.6
Pop that into a calculator and you get:
30/0.6 = 50
This doesn’t work for integers, however:
30/3 = 30 * 1/3
30/3 = 10
30 * 1/3 = 30/3 = 10
For a denominator that is just an integer, dividing by that number is the same as multiplying it by its reciprocal. Thus, dividing a number by 3 is the same as multiplying it by 1/3. Going back to the example we explored above when the denominator is a fraction you can multiply the numerator by the inverse of that fraction (instead of dividing by the original) to get the same result
