4-95. What fraction of one hour ( 60 minutes) is represented by the following numbers of minutes? Simplify each fraction whenever possible. A sketch of a clock might help you. 10 minutes a) 15 minutes b) 30 minutes c) 20 minutes

To find what fraction of one hour (60 minutes) is represented by the given numbers of minutes, we can use the formula: \[ \text{Fraction} = \frac{\text{Number of minutes}}{60} \] We will simplify each fraction whenever possible. ### a) 10 minutes \[ \text{Fraction} = \frac{10}{60} \] To simplify, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 10: \[ \frac{10 \div 10}{60 \div 10} = \frac{1}{6} \] ### b) 15 minutes \[ \text{Fraction} = \frac{15}{60} \] The GCD of 15 and 60 is 15: \[ \frac{15 \div 15}{60 \div 15} = \frac{1}{4} \] ### c) 30 minutes \[ \text{Fraction} = \frac{30}{60} \] The GCD of 30 and 60 is 30: \[ \frac{30 \div 30}{60 \div 30} = \frac{1}{2} \] ### d) 20 minutes \[ \text{Fraction} = \frac{20}{60} \] The GCD of 20 and 60 is 20: \[ \frac{20 \div 20}{60 \div 20} = \frac{1}{3} \] ### Summary of Results - 10 minutes: \(\frac{1}{6}\) - 15 minutes: \(\frac{1}{4}\) - 30 minutes: \(\frac{1}{2}\) - 20 minutes: \(\frac{1}{3}\) These fractions represent the portions of one hour for the respective minutes.