Question

which is the value of (\frac{1}{8} \times \frac{1}{2} + \frac{3}{4} div \frac{1}{2})? express your answer in lowest terms. select an answer a (1\frac{9}{16}) b (\frac{5}{16}) c (1\frac{5}{18}) d (\frac{7}{18})

Explanation:

Step1: Calculate multiplication and division

First, calculate \(\frac{1}{8} \times \frac{1}{2}\) and \(\frac{3}{4} \div \frac{1}{2}\) separately.
For \(\frac{1}{8} \times \frac{1}{2}\), multiply the numerators and denominators: \(\frac{1 \times 1}{8 \times 2} = \frac{1}{16}\).
For \(\frac{3}{4} \div \frac{1}{2}\), divide by a fraction is multiply by its reciprocal: \(\frac{3}{4} \times 2 = \frac{3 \times 2}{4} = \frac{6}{4} = \frac{3}{2}\).

Step2: Add the results

Now add \(\frac{1}{16}\) and \(\frac{3}{2}\). First, find a common denominator, which is 16. Convert \(\frac{3}{2}\) to sixteenths: \(\frac{3}{2} = \frac{3 \times 8}{2 \times 8} = \frac{24}{16}\).
Then add: \(\frac{1}{16} + \frac{24}{16} = \frac{1 + 24}{16} = \frac{25}{16}\).
Convert \(\frac{25}{16}\) to a mixed number: \(1\frac{9}{16}\).

Answer:

A. \(1\frac{9}{16}\)