Question

Write the numbers from $1$ to $20$.

(i) What fractions of them are even numbers?

(ii) What fractions of them are odd numbers?

(iii) Are these fractions equal?

Answer 1

The twenty numbers from $1$to $20$ are :

$1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20$.

(i)

The even numbers from $1$ to $20$ are :

$2,4,6,8,10,12,14,16,18,20$.

Clearly, there are $10$ even numbers among $20$ total numbers. Hence, fraction of even $10$ numbers among $20$ total numbers is $\frac{10}{20}$.

(ii)

The odd numbers from $1$ to $20$ are :

$1,3,5,7,9,11,13,15,17,19$

Again, there are $10$ odd numbers among $20$ total numbers. Hence, fraction of odd $10$ numbers among $20$ total numbers is $\frac{10}{20}$

(iii)

From (i) and (ii), we have

Fraction of even numbers $=\frac{10}{20}$

and Fraction of odd numbers $=\frac{10}{20}$

From above two, we conclude that both the fractions are equal.