We need to solve the subtraction problem $\frac{10}{3} - \frac{4}{5}$ by finding a common denominator and simplifying the resulting fraction. The common denominator is given as 15.

1. Problem Description

We need to solve the subtraction problem $\frac{10}{3} - \frac{4}{5}$ by finding a common denominator and simplifying the resulting fraction. The common denominator is given as

1

5.

2. Solution Steps

First, we convert both fractions to have a common denominator of

1

5. To convert $\frac{10}{3}$ to a fraction with denominator 15, we multiply both the numerator and the denominator by 5:

$\frac{10}{3} = \frac{10 \times 5}{3 \times 5} = \frac{50}{15}$

To convert $\frac{4}{5}$ to a fraction with denominator 15, we multiply both the numerator and the denominator by 3:

$\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}$

Now we can subtract the fractions:

$\frac{50}{15} - \frac{12}{15} = \frac{50 - 12}{15} = \frac{38}{15}$

The fraction $\frac{38}{15}$ is already in simplest form. We can also convert this improper fraction to a mixed number. $38 \div 15 = 2$ with a remainder of

8. So, $\frac{38}{15} = 2\frac{8}{15}$.

3. Final Answer

$\frac{10}{3} - \frac{4}{5} = \frac{50}{15} - \frac{12}{15} = \frac{38}{15} = 2 \frac{8}{15}$

The boxes should be filled in as follows:

50

12

38

15

2

8

15