Question

katya is making a rectangular table that is \\(\frac{3}{4}\\) m wide. the table has an area of \\(1\frac{1}{5}\\) m². how long is the table? \\(\square\\) m

Explanation:

Step1: Recall the area formula for a rectangle

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

Step2: Convert the mixed number to an improper fraction

The area \( A = 1\frac{1}{5}\,m^2 \). To convert this mixed number to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 1\frac{1}{5}=\frac{1\times5 + 1}{5}=\frac{6}{5} \).

Step3: Substitute the values into the formula for length

We know \( A=\frac{6}{5}\,m^2 \) and \( w = \frac{3}{4}\,m \). Substituting into \( l=\frac{A}{w} \), we get \( l=\frac{\frac{6}{5}}{\frac{3}{4}} \).

Step4: Divide the fractions

Dividing by a fraction is the same as multiplying by its reciprocal. So, \( \frac{\frac{6}{5}}{\frac{3}{4}}=\frac{6}{5}\times\frac{4}{3} \).

Step5: Simplify the multiplication

Simplify the numerators and denominators. \( 6 \) and \( 3 \) have a common factor of \( 3 \), so \( \frac{6\div3}{5}\times\frac{4}{3\div3}=\frac{2}{5}\times\frac{4}{1}=\frac{8}{5} \).

Step6: Convert the improper fraction to a mixed number (optional)

\( \frac{8}{5}=1\frac{3}{5} \).

Answer:

\( 1\frac{3}{5} \) (or \( \frac{8}{5} \))