Questions: Compute the following: Answer as a fraction (or improper fraction) in simplest form. 3 1/3 ÷ 8 1/2

Solution Steps

To solve the division of mixed numbers, first convert the mixed numbers to improper fractions. Then, divide the first fraction by the second by multiplying the first fraction by the reciprocal of the second. Finally, simplify the resulting fraction to its simplest form.

To divide the mixed numbers \(3 \frac{1}{3}\) and \(8 \frac{1}{2}\), we first convert them to improper fractions.

For \(3 \frac{1}{3}\): \[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3} \]

For \(8 \frac{1}{2}\): \[ 8 \frac{1}{2} = \frac{8 \times 2 + 1}{2} = \frac{17}{2} \]

To divide \(\frac{10}{3}\) by \(\frac{17}{2}\), multiply \(\frac{10}{3}\) by the reciprocal of \(\frac{17}{2}\), which is \(\frac{2}{17}\).

\[ \frac{10}{3} \div \frac{17}{2} = \frac{10}{3} \times \frac{2}{17} = \frac{10 \times 2}{3 \times 17} = \frac{20}{51} \]

The fraction \(\frac{20}{51}\) is already in its simplest form, as 20 and 51 have no common factors other than 1.

Final Answer