Questions: Evaluate the following expressions. a. 2/3 × 5/8 b. 1/2 + 1/10 a. 2/3 × 5/8 = 5/12 (Type an integer or a simplified fraction.) b. 1/2 + 1/10 = (Type an integer or a simplified fraction.)

Solution Steps

To solve the given expressions, we need to perform basic arithmetic operations on fractions. For part (a), we multiply the numerators and denominators of the fractions. For part (b), we find a common denominator and then add the fractions.

1. For part (a), multiply the numerators and the denominators of the fractions.
2. For part (b), find a common denominator, convert the fractions, and then add them.

To evaluate \(\frac{2}{3} \times \frac{5}{8}\), we multiply the numerators and the denominators: \[ \frac{2 \times 5}{3 \times 8} = \frac{10}{24} \] Simplify \(\frac{10}{24}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2: \[ \frac{10 \div 2}{24 \div 2} = \frac{5}{12} \]

To evaluate \(\frac{1}{2} + \frac{1}{10}\), we first find a common denominator. The least common multiple of 2 and 10 is 10. Convert each fraction: \[ \frac{1}{2} = \frac{5}{10} \] \[ \frac{1}{10} = \frac{1}{10} \] Now add the fractions: \[ \frac{5}{10} + \frac{1}{10} = \frac{5 + 1}{10} = \frac{6}{10} \] Simplify \(\frac{6}{10}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2: \[ \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \]

Final Answer