Question

Give a proper fraction whose denominator is $4$ more than the numerator. How many are they?

Answer 1

Let's find fractions whose denominator is $4$ more than the numerator:

A fraction whose numerator is less than the denominator is called a proper fraction.

Let's try to find pair of numbers whose difference is $4$:

$9-5=4$ ( here $5<9$ ), the proper fraction $=\frac{5}{9}$

$10-6=4$ ( here $6<10$ ), the proper fraction $=\frac{6}{10}$

$7-3=4$ ( here $3<7$ ), the proper fraction $=\frac{3}{7}$

$5-1=4$ ( here $1<5$ ), the proper fraction $=\frac{1}{5}$

So, we see that there can be infinite such pairs.

Hence, proper fractions whose denominator is $4$ more than the numerator are $\frac{5}{9}$, $\frac{6}{10}$, $\frac{3}{7}$ and $\frac{1}{5}$. They are infinite in number.