Question

a carpenter uses \\(\frac{1}{4}\\) of a wooden dowel rod to make each chair leg. how many chair legs can the carpenter make with \\(\frac{9}{10}\\) of a dowel rod? \\(\circ\\) a. \\(\frac{5}{18}\\) \\(\circ\\) b. \\(\frac{9}{40}\\) \\(\circ\\) c. \\(3\frac{3}{5}\\) \\(\circ\\) d. \\(4\frac{4}{9}\\)

Explanation:

Step1: Understand the problem

We need to find out how many times \(\frac{1}{4}\) fits into \(\frac{9}{10}\), which means we have to divide \(\frac{9}{10}\) by \(\frac{1}{4}\).

Step2: Divide the fractions

To divide a fraction by another fraction, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of \(\frac{1}{4}\) is \(4\). So we calculate \(\frac{9}{10} \div \frac{1}{4}=\frac{9}{10} \times 4\).

Step3: Multiply the fractions

\(\frac{9}{10} \times 4=\frac{9\times4}{10}=\frac{36}{10}\).

Step4: Simplify the fraction

Simplify \(\frac{36}{10}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(2\). So \(\frac{36\div2}{10\div2}=\frac{18}{5}\).

Step5: Convert to mixed number

Convert \(\frac{18}{5}\) to a mixed number. \(18\div5 = 3\) with a remainder of \(3\), so \(\frac{18}{5}=3\frac{3}{5}\).

Answer:

C. \(3\frac{3}{5}\)