Question

Give a proper fraction whose numerator and denominator add up to$10$. How many fractions can be made?

Answer 1

Finding the proper fractions

A fraction is known as a proper fraction if its numerator is less than the denominator.

Here, the proper fraction has to be made such that:

$1)$ Numerator $<$ denominator

$2)$ Numerator $+$ denominator $=10$

Now, $\frac{1}{9}$ is a fraction such that

$1)$ $1<9$

$2)$ $1+9=10$.

Therefore, $\frac{1}{9}$ is the required proper fraction.

The other fractions which satisfy the above two conditions are $\frac{2}{8},\frac{3}{7}$ and $\frac{4}{6}$.

Hence, there are only four proper rational fractions with the sum of numerator and denominator as $10$.