Question

What is the value of \[\left( \dfrac{\dfrac{2}{3}-\dfrac{5}{6}}{\dfrac{3}{4}} \right)\]?

Answer 1

Hint: In this problem, we have to simplify the given fraction and write the answer. We can see that in the numerator, the given fraction does not have a similar denominator and so we cannot subtract it directly. We can now cross multiply the given fractions in the numerator and simplify the terms, we will get a simplified form, we will have a fraction in the numerator and the denominator, where we can perform the reciprocal method to get the final answer.

Complete step-by-step solution:
We know that the given fraction is,
\[\left( \dfrac{\dfrac{2}{3}-\dfrac{5}{6}}{\dfrac{3}{4}} \right)\]
We can now see that the numerator given fraction has two fractions in it which cannot be directly subtracted as it does not have a similar denominator.
We can now use the cross-multiplication method for the fractions in the numerator, we get
\[\Rightarrow \dfrac{\dfrac{2\left( 6 \right)-5\left( 3 \right)}{6\times 3}}{\dfrac{3}{4}}\]
We can now multiply the terms inside the bracket in both the numerator, we get
\[\Rightarrow \dfrac{\dfrac{12-15}{18}}{\dfrac{3}{4}}=\dfrac{-\dfrac{1}{6}}{\dfrac{3}{4}}\]
We can now take the reciprocal for the above step, by changing the terms in the numerator and the denominator in the numerator and multiplying it with the numerator of the problem, we get
\[\Rightarrow -\dfrac{1}{6}\times \dfrac{4}{3}= -\dfrac{2}{9}\]
Therefore, the value of the given fraction \[\left( \dfrac{\dfrac{2}{3}-\dfrac{5}{6}}{\dfrac{3}{4}} \right)\] is \[-\dfrac{2}{9}\].

Note: Students make mistakes while cross multiplying the term, where we should cross multiply the numerators and denominators respectively and the both denominators. we should know that we cannot subtract the fraction directly as it has different denominators, so that we have to cross multiply the fraction to get the simplified form.