Question

Give the proper fraction:

Whose numerator and denominator add up to $10$. how many fraction of this kind can you make?

Answer 1

According to the question we have to find out the possible fractions whose numerator and denominator when added up will sum upto $10$

Since we have $9$ digits so $9$ possible combination can be there.

The $9$ distinct digits are: $1,2,3,4,5,6,7,8,9.$

The pairs for sum of $10$ can be $(1,9),(2,8),(3,7),(4,6),(5,5),(6,4),(7,3),(8,2),(9,1).$

Therefore these pairs can form fraction to satisfy the condition given in the question.

Hence the$9$ fractions are:

$\frac{1}{9},\frac{2}{8},\frac{3}{7},\frac{4}{6},\frac{5}{5},\frac{6}{4}\frac{7}{3}\frac{8}{2}\frac{9}{1}$

Hence, the required fraction are $\frac{1}{9},\frac{2}{8},\frac{3}{7},\frac{4}{6},\frac{5}{5},\frac{6}{4}\frac{7}{3}\frac{8}{2}\frac{9}{1}$

Hence, there are $9$ such fraction.