We need to solve the subtraction problem involving mixed numbers: $14\frac{2}{5} - 5\frac{9}{10}$.

1. Problem Description

We need to solve the subtraction problem involving mixed numbers: $14\frac{2}{5} - 5\frac{9}{10}$.

2. Solution Steps

First, convert the mixed numbers to improper fractions.

$14\frac{2}{5} = \frac{(14 \times 5) + 2}{5} = \frac{70 + 2}{5} = \frac{72}{5}$

$5\frac{9}{10} = \frac{(5 \times 10) + 9}{10} = \frac{50 + 9}{10} = \frac{59}{10}$

Now, we need to subtract the two improper fractions: $\frac{72}{5} - \frac{59}{10}$. To do this, we need a common denominator. The least common multiple of 5 and 10 is

1

0. So, we convert $\frac{72}{5}$ to an equivalent fraction with a denominator of

1

0.

$\frac{72}{5} = \frac{72 \times 2}{5 \times 2} = \frac{144}{10}$

Now, we can perform the subtraction:

$\frac{144}{10} - \frac{59}{10} = \frac{144 - 59}{10} = \frac{85}{10}$

Simplify the fraction:

$\frac{85}{10} = \frac{17 \times 5}{2 \times 5} = \frac{17}{2}$

Convert the improper fraction $\frac{17}{2}$ to a mixed number:

$\frac{17}{2} = 8\frac{1}{2}$ (since $17 \div 2 = 8$ with a remainder of 1).

3. Final Answer

$8\frac{1}{2}$