Question

Give a proper fraction whose numerator and denominator add upto $10$. How many are they?

Answer 1

Let's find fractions whose numerator and denominator add upto $10$:

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

Let's try to break $10$ into two parts such that the first part is smaller than the second part:

$1+9=10$ ( here $1<9$ ), the proper fraction $=\frac{1}{9}$

$2+8=10$ ( here $2<8$ ), the proper fraction $=\frac{2}{8}$

$3+7=10$ ( here $3<7$ ), the proper fraction $=\frac{3}{7}$

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

Hence, proper fractions whose numerator and denominator add upto $10$ are $\frac{1}{9}$, $\frac{2}{8}$, $\frac{3}{7}$ and $\frac{4}{6}$. They are $4$ in number.