Question

In class VI, out of $80$ students, $20$ students play table tennis , $25$ students play cricket and $15$ students play football. The rest of the students do not play any game. What fraction of students do not play any game? Also, find what fraction of students play cricket?

Answer 1

Hint: Firstly find out the total number of students who do not play any game by subtracting the sum of the number of students who play games from the total number of students in the class. Then find the fractions as required in the question using data given.

Complete step-by-step answer:
Given the information in the question is that there are a total of $80$ students in the class, number of students who play table tennis is $20$, number of students who play cricket is $25$ and number of students who play football is $15$.
And the rest of the students do not play any game, i.e. the sum of students who play table tennis, cricket and football subtracted from total students will be the number of students who do not play any game.
$ \Rightarrow $ Number of students who play no game$ = $ Total students in class$ - $ Sum of the number of students who play any of the game
$ \Rightarrow $ Number of the student who plays no game$ = 80 - \left( {20 + 25 + 15} \right) = 80 - 60 = 20$
Now let’s understand the concept of fraction. A fraction is a representation of a quantity from the whole. It gives the measure of the quantity of a part from its whole
So, the fraction of student who does not play any game will be written as the division of the number of students who do not play any game by the total number of students in the class
$ \Rightarrow $ The fraction of students who do not play a game$ = \dfrac{{20}}{{80}} = \dfrac{2}{8} = \dfrac{1}{4}$
Similarly, the fraction of students who play cricket will be written as the division of the number of students who play cricket by the total number of students in the class.
$ \Rightarrow $ The fraction of students who play cricket$ = \dfrac{{25}}{{80}} = \dfrac{5}{{16}}$

Note:For solving problems like these you need to understand the concept of a fraction and how to calculate a fraction. Remember, a fraction should always be represented in its simplest form, i.e. numerator and denominator can only have $1$ as their common factor.