Question: Perform the indicated operation and simplify the result. \frac{7}{35} \cdot \frac{21}{10} =…

Perform the indicated operation and simplify the result. \frac{7}{35} \cdot \frac{21}{10} = \boxed{\quad} (Type a simplified fraction.)

Solution

The problem is to multiply the fractions and simplify the result. First, multiply the numerators: \[ 7 \times 21 = 147 \] Next, multiply the denominators: \[ 35 \times 10 = 350 \] Now, form the fraction: \[ \frac{147}{350} \] To simplify, find the greatest common divisor (GCD) of 147 and 350. The GCD is 7. Divide both the numerator and the denominator by their GCD: \[ \frac{147 \div 7}{350 \div 7} = \frac{21}{50} \] So, the simplified fraction is: \[ \frac{21}{50} \]