Calculate the following fractions 1. \( \frac{3}{10} \times \frac{5}{27} \) 2. \( \frac{50}{200} \times \frac{140}{150} \)
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To solve the first fraction \( \frac{3}{10} \times \frac{5}{27} \), you simply multiply the numerators and the denominators: \[ \frac{3 \times 5}{10 \times 27} = \frac{15}{270} \] Now, simplify \( \frac{15}{270} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 15: \[ \frac{15 \div 15}{270 \div 15} = \frac{1}{18} \] For the second fraction \( \frac{50}{200} \times \frac{140}{150} \), again, start by multiplying the numerators and the denominators: \[ \frac{50 \times 140}{200 \times 150} = \frac{7000}{30000} \] Next, simplify \( \frac{7000}{30000} \) by dividing both by their GCD, which is 1000: \[ \frac{7000 \div 1000}{30000 \div 1000} = \frac{7}{30} \] So the final answers are: 1. \( \frac{1}{18} \) 2. \( \frac{7}{30} \)
