1 13/15 • 5/8 2 2/5

To solve the expression \(1 \frac{13}{15} \cdot \frac{5}{8} \cdot 2 \frac{2}{5}\), we will first convert the mixed numbers to improper fractions.

1. Convert \(1 \frac{13}{15}\) to an improper fraction: \[ 1 \frac{13}{15} = \frac{1 \times 15 + 13}{15} = \frac{15 + 13}{15} = \frac{28}{15} \]

2. Convert \(2 \frac{2}{5}\) to an improper fraction: \[ 2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} \]

Now we can rewrite the expression using these improper fractions: \[ \frac{28}{15} \cdot \frac{5}{8} \cdot \frac{12}{5} \]

Next, we can simplify before multiplying:

1. The \(\frac{5}{5}\) cancels out: \[ \frac{28}{15} \cdot \frac{1}{8} \cdot \frac{12}{1} \]

Now, we multiply: \[ \frac{28 \cdot 1 \cdot 12}{15 \cdot 8 \cdot 1} = \frac{336}{120} \]

Now, we simplify \(\frac{336}{120}\):

• Find the GCD of 336 and 120. We can divide both by 24 (the GCD): \[ \frac{336 \div 24}{120 \div 24} = \frac{14}{5} \]

Therefore, \[ 1 \frac{13}{15} \cdot \frac{5}{8} \cdot 2 \frac{2}{5} = \frac{14}{5} \]

If you want to convert \(\frac{14}{5}\) back to a mixed number, it would be: \[ 2 \frac{4}{5} \]

So the final answer is: \[ \frac{14}{5} \text{ or } 2 \frac{4}{5} \]