Question

Write down ten positive rational numbers such that the sum of the numerator and the denominator of each is $11$. Write them in decreasing order

Answer 1

Firstly, let us determine the numbers whose sum is $11$ as follows:

$10+1,9+2,8+3,7+4,6+5,5+6,4+7,3+8,2+9$ and $1+10$

Now, the ten positive rational numbers in which the sum of the numerator and denominator is $11$ are:

$\frac{10}{1},\frac{9}{2},\frac{8}{3},\frac{7}{4},\frac{6}{5},\frac{5}{6},\frac{4}{7},\frac{3}{8},\frac{2}{9},\frac{1}{10}$

Hence, the decreasing order of the numbers is $\frac{10}{1},\frac{9}{2},\frac{8}{3},\frac{7}{4},\frac{6}{5},\frac{5}{6},\frac{4}{7},\frac{3}{8},\frac{2}{9},\frac{1}{10}$.