Question

A painter is required to make 21 portraits for a business tycoon. He has already made 14 of them. What fraction of the total portraits he has made so far?

Answer 1

Hint: Assume the total number of portraits of the business tycoon needed to be made by the painter as y and the total number of portraits he has already made as x. now, to find the fraction of the number of portraits the painter has made, divide x by y and cancel the common factors to get the answer in the simplest form of the fraction.

Complete step by step answer:
Here we have been provided with the information regarding the number of paintings to be made by the painter and we are asked to find the required fraction. First we need to understand the term ‘fraction’.
Now, in mathematics the fraction is the ratio of a part of something to its whole. For example: - we have an apple whose 10 slices we have made. Now, if we eat 3 slices so the fraction of the slices we ate will be equal to the ratio of 3 and 10.
Let us come to the question, we have been told in the question that the painter has to make a total of 14 painting of the business tycoon out of which he has already make 14 paintings, therefore the fraction of the total portraits he has made will be equal to the ratio of 14 and 21, so we get,
$\Rightarrow $ Fraction of the portraits the painter has made = $\dfrac{14}{21}$
Cancelling the common factors we get,
$\therefore $ Fraction of the portraits the painter has made = $\dfrac{2}{3}$
Hence, the required fraction is $\dfrac{2}{3}$.

Note: Note that if you are asked further what fraction of the portraits is left to be made then there are two processes to get the answer. The first one is, find the number of portraits to be made and divide it by 21. The second process is easier and preferred more, subtract the obtained fraction $\dfrac{2}{3}$ from 1 to get the answer.