Question

How do you divide $ \dfrac{7}{{24}} $ by $ \dfrac{{35}}{{48}} $ and reduce the quotient to lowest fraction ?

Answer 1

Hint: As we can clearly see that the expression given in the question here means $ \dfrac{7}{{24}} $ divided by $ \dfrac{{35}}{{48}} $ . Whenever we see a question like this, our approach should be to simplify it. Thus, we need to expand it and then multiply $ \dfrac{7}{{24}} $ with the reciprocal of $ \dfrac{{35}}{{48}} $ so that if there are digits which can be cut through the numerator and the denominator, they will get cut and the rest will be multiplied straight cross to obtain the answer.

Complete step-by-step answer:
So, in the required question, we are required to find the quotient when $ \dfrac{7}{{24}} $ is divided by $ \dfrac{{35}}{{48}} $ and reduce it to lowest form.
So, $ \dfrac{{\left( {\dfrac{7}{{24}}} \right)}}{{\left( {\dfrac{{35}}{{48}}} \right)}} $
As we know that $ \dfrac{a}{b} $ means $ a $ divided by $ b $ , the expression given in the question means the same as:
 $ \dfrac{{\left( {\dfrac{7}{{24}}} \right)}}{{\left( {\dfrac{{35}}{{48}}} \right)}} $
So, We can multiply $ \dfrac{7}{{24}} $ with the reciprocal of $ \dfrac{{35}}{{48}} $ to perform the required task and find the quotient.
So, $ \dfrac{7}{{24}} \times \dfrac{{48}}{{35}} $
So, cancelling the common terms in the numerator and denominator, we get,
 $ \Rightarrow \dfrac{2}{5} $
So, the quotient obtained on dividing $ \dfrac{7}{{24}} $ by $ \dfrac{{35}}{{48}} $ is $ \left( {\dfrac{2}{5}} \right) $ .
So, the correct answer is “ $ \left( {\dfrac{2}{5}} \right) $ ”.

Note: In a fraction, numerator and denominator never get cancelled in division. They only get cut in multiplication. Also, here we see that we can turn division into simple multiplication. In case, we have to divide a number by another number, what we can do is to simply multiply the first number by the inverse of the second. This rule could also be directly used to solve questions like this. The answer obtained would have remained the same. Lastly, it is good to convert your answer from improper fraction to mixed fraction even if it is not mentioned in the question.