Question

solving problems with fractions
check your understanding- question 4 of 5
the area of a rectangle is \\(\frac{1}{16}\\) square meter. the length is \\(\frac{1}{10}\\) meter.
what is the width of the rectangle?
\\(\bigcirc\\) a. \\(\frac{5}{16}\\) meter
\\(\bigcirc\\) b. \\(\frac{1}{160}\\) meter
\\(\bigcirc\\) c. \\(\frac{5}{8}\\) meter
\\(\bigcirc\\) d. \\(\frac{8}{5}\\) meter

Explanation:

Step1: Recall the formula for the area of a rectangle

The area \( A \) of a rectangle is given by the formula \( A = l \times w \), where \( l \) is the length and \( w \) is the width. We need to solve for \( w \), so we can rearrange the formula to \( w=\frac{A}{l} \).

Step2: Substitute the given values into the formula

We know that \( A = \frac{1}{16} \) square meter and \( l=\frac{1}{10} \) meter. Substituting these values into the formula for \( w \), we get \( w=\frac{\frac{1}{16}}{\frac{1}{10}} \).

Step3: Divide the fractions

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So, \( \frac{\frac{1}{16}}{\frac{1}{10}}=\frac{1}{16}\times\frac{10}{1} \).

Step4: Simplify the multiplication

Multiplying the numerators and denominators, we have \( \frac{1\times10}{16\times1}=\frac{10}{16} \). Then, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \( \frac{10\div2}{16\div2}=\frac{5}{8} \).

Answer:

C. $\frac{5}{8}$ meter