Ex 13.3 \( -\frac{9}{7} \times \frac{-5}{12} \) Calculate \( \frac{4}{5} \) of \( 125 \times \frac{7}{4} \times 2 \frac{1}{7} \)

Calculate the value by following steps: - step0: Calculate: \(-\frac{9}{7}\times \frac{-5}{12}\) - step1: Rewrite the fraction: \(-\frac{9}{7}\left(-\frac{5}{12}\right)\) - step2: Use the rules for multiplication and division: \(\frac{9}{7}\times \frac{5}{12}\) - step3: Reduce the numbers: \(\frac{3}{7}\times \frac{5}{4}\) - step4: Multiply the fractions: \(\frac{3\times 5}{7\times 4}\) - step5: Multiply: \(\frac{15}{28}\) Calculate or simplify the expression \( \frac{4}{5} \times 125 \times \frac{7}{4} \times 2 + \frac{1}{7} \). Calculate the value by following steps: - step0: Calculate: \(\frac{4}{5}\times 125\times \frac{7}{4}\times 2+\frac{1}{7}\) - step1: Multiply the terms: \(350+\frac{1}{7}\) - step2: Reduce fractions to a common denominator: \(\frac{350\times 7}{7}+\frac{1}{7}\) - step3: Transform the expression: \(\frac{350\times 7+1}{7}\) - step4: Multiply the numbers: \(\frac{2450+1}{7}\) - step5: Add the numbers: \(\frac{2451}{7}\) Let's solve the two parts of your problem step by step. ### Part 1: Calculate \( -\frac{9}{7} \times \frac{-5}{12} \) 1. **Multiply the fractions**: \[ -\frac{9}{7} \times \frac{-5}{12} = \frac{9 \times 5}{7 \times 12} = \frac{45}{84} \] 2. **Simplify the fraction**: - The greatest common divisor (GCD) of 45 and 84 is 3. - Dividing both the numerator and the denominator by 3: \[ \frac{45 \div 3}{84 \div 3} = \frac{15}{28} \] Thus, the result of \( -\frac{9}{7} \times \frac{-5}{12} \) is \( \frac{15}{28} \) or approximately \( 0.5357142857 \). ### Part 2: Calculate \( \frac{4}{5} \) of \( 125 \times \frac{7}{4} \times 2 \frac{1}{7} \) 1. **Convert \( 2 \frac{1}{7} \) to an improper fraction**: \[ 2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{14 + 1}{7} = \frac{15}{7} \] 2. **Calculate the expression**: \[ 125 \times \frac{7}{4} \times \frac{15}{7} \] - The \( \frac{7}{4} \) and \( \frac{15}{7} \) can be simplified: \[ \frac{7}{4} \times \frac{15}{7} = \frac{15}{4} \] - Now multiply by 125: \[ 125 \times \frac{15}{4} = \frac{125 \times 15}{4} = \frac{1875}{4} \] 3. **Calculate \( \frac{4}{5} \) of \( \frac{1875}{4} \)**: \[ \frac{4}{5} \times \frac{1875}{4} = \frac{1875}{5} = 375 \] Thus, the result of \( \frac{4}{5} \) of \( 125 \times \frac{7}{4} \times 2 \frac{1}{7} \) is \( 375 \). ### Final Results: - \( -\frac{9}{7} \times \frac{-5}{12} = \frac{15}{28} \) - \( \frac{4}{5} \) of \( 125 \times \frac{7}{4} \times 2 \frac{1}{7} = 375 \)