Let's break down and solve the equation step by step:

We are given:

$4 \frac{2}{3} + 3 \frac{4}{5} = 8 \frac{7}{15}$

Step 1: Convert mixed numbers into improper fractions.

$4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{14}{3}$ $3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{19}{5}$

Step 2: Add the two improper fractions.

We need to find the least common denominator (LCD) of 3 and 5, which is 15. So, we rewrite the fractions with a denominator of 15:

$\frac{14}{3} = \frac{14 \times 5}{3 \times 5} = \frac{70}{15}$ $\frac{19}{5} = \frac{19 \times 3}{5 \times 3} = \frac{57}{15}$

Now, add the two fractions:

$\frac{70}{15} + \frac{57}{15} = \frac{70 + 57}{15} = \frac{127}{15}$

Step 3: Convert the improper fraction back into a mixed number.

$\frac{127}{15} = 8 \frac{7}{15}$

So, the left-hand side of the equation simplifies to:

$4 \frac{2}{3} + 3 \frac{4}{5} = 8 \frac{7}{15}$

Thus, the given equation is correct.

Would you like further details or have any questions?

Here are 5 related questions you can explore:

1. How do you subtract mixed numbers with different denominators?
2. How can you simplify improper fractions?
3. What is the process for converting improper fractions into mixed numbers?
4. How do you find the least common denominator (LCD) for three fractions?
5. Can mixed numbers be multiplied directly, or must they be converted first?

Tip: Always convert mixed numbers to improper fractions when adding or subtracting for easier calculation.