Evalkit \( 7 \frac{7}{15}-2 \frac{2}{3}+1 \frac{5}{1} \)

To solve the expression \( 7 \frac{7}{15}-2 \frac{2}{3}+1 \frac{5}{1} \), let's first convert all mixed numbers to improper fractions: 1. For \( 7 \frac{7}{15} \): \[ 7 \frac{7}{15} = \frac{7 \times 15 + 7}{15} = \frac{105 + 7}{15} = \frac{112}{15} \] 2. For \( 2 \frac{2}{3} \): \[ 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \] 3. For \( 1 \frac{5}{1} \): This is simply \( 1 \frac{5}{1} = 1 + 5 = 6 \), which can also be written as \( \frac{6}{1} \) or \( \frac{6 \times 1}{1} = \frac{6}{1} \). Now we rewrite the expression with improper fractions: \[ \frac{112}{15} - \frac{8}{3} + 6 \] Next, we convert all terms to have a common denominator. The least common denominator of 15 and 3 is 15. We convert \( 6 \) into a fraction: \[ 6 = \frac{6 \times 15}{15} = \frac{90}{15} \] Now we rewrite the expression: \[ \frac{112}{15} - \frac{8 \times 5}{15} + \frac{90}{15} \] This simplifies to: \[ \frac{112}{15} - \frac{40}{15} + \frac{90}{15} \] Now combine the three fractions: \[ \frac{112 - 40 + 90}{15} = \frac{162}{15} \] Finally, simplify \( \frac{162}{15} \): \[ \frac{162 \div 3}{15 \div 3} = \frac{54}{5} \] Convert \( \frac{54}{5} \) back to a mixed number: \[ 54 \div 5 = 10 \quad \text{(remainder: } 4\text{)} \] Thus, it is \( 10 \frac{4}{5} \). The final answer is: \[ \boxed{10 \frac{4}{5}} \]