The expression in the image is:

$4 \frac{1}{3} + 3 \frac{2}{5} - 2 \frac{14}{15}$

Let's break this down step-by-step.

Step 1: Convert the mixed numbers into improper fractions

1. $4 \frac{1}{3} = \frac{13}{3}$
2. $3 \frac{2}{5} = \frac{17}{5}$
3. $2 \frac{14}{15} = \frac{44}{15}$

Step 2: Find a common denominator

The denominators are 3, 5, and 15. The least common denominator (LCD) is 15.

• $\frac{13}{3} = \frac{65}{15}$
• $\frac{17}{5} = \frac{51}{15}$
• $\frac{44}{15} = \frac{44}{15}$ (no change)

Step 3: Perform the addition and subtraction

Now, we can add and subtract the fractions:

$\frac{65}{15} + \frac{51}{15} - \frac{44}{15} = \frac{65 + 51 - 44}{15} = \frac{72}{15}$

Step 4: Simplify the result

$\frac{72}{15} = 4 \frac{12}{15} = 4 \frac{4}{5}$

Thus, the result of the expression is:

$4 \frac{4}{5}$

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How do you find the least common denominator of three numbers?
2. What is the process for converting a mixed number to an improper fraction?
3. How can improper fractions be added and subtracted easily?
4. Why is it necessary to simplify fractions after solving?
5. What are some other ways to solve mixed-number operations?

Tip: Always check if fractions can be simplified after performing operations to get the final result in its simplest form.