10. Find the missing numbers \[ 2 \frac{2}{5}+\square \frac{\square}{15}=7 \frac{4}{15} \]

To solve for the missing numbers in the equation \( 2 \frac{2}{5} + \square \frac{\square}{15} = 7 \frac{4}{15} \), let's first convert all the mixed numbers to improper fractions. 1. Convert \( 2 \frac{2}{5} \) to an improper fraction: \[ 2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} \] 2. Convert \( 7 \frac{4}{15} \) to an improper fraction: \[ 7 \frac{4}{15} = \frac{7 \times 15 + 4}{15} = \frac{105 + 4}{15} = \frac{109}{15} \] Now, we can rewrite the equation as: \[ \frac{12}{5} + \square \frac{\square}{15} = \frac{109}{15} \] Next, we need to isolate the square term \(\square \frac{\square}{15}\): \[ \square \frac{\square}{15} = \frac{109}{15} - \frac{12}{5} \] To subtract these fractions, we need a common denominator. The least common multiple of 5 and 15 is 15. Therefore, we convert \(\frac{12}{5}\) to have a denominator of 15: \[ \frac{12}{5} = \frac{12 \times 3}{5 \times 3} = \frac{36}{15} \] Now we substitute this into the equation: \[ \square \frac{\square}{15} = \frac{109}{15} - \frac{36}{15} = \frac{109 - 36}{15} = \frac{73}{15} \] At this point, we know that: \[ \square \frac{\square}{15} = \frac{73}{15} \] To express \(\square \frac{\square}{15}\) as an improper fraction, we identify the missing numbers. The first square corresponds to the integer part, which we can denote as \(a\). The second square corresponds to the numerator, denoted as \(b\). We can express it as: \[ a \frac{b}{15} = \frac{a \times 15 + b}{15} \] We set this equal to \(\frac{73}{15}\): \[ a \times 15 + b = 73 \] We can determine integer values for \(a\) and \(b\) by trial. Starting with \(a = 4\): \[ 4 \times 15 + b = 73 \implies 60 + b = 73 \implies b = 13 \] Thus, we find: \[ \square = 4 \quad \text{and} \quad \square = 13 \] Finally, the missing numbers are: \[ 4 \frac{13}{15} \] Overall, we conclude that: \[ \boxed{4 \quad 13} \]