Question

1. a rectangle has a length of $3\frac{7}{8}$ inches and an area of $6\frac{15}{16}$ square inches. write an equation that represents the area of the rectangle in terms of its length and width, $w$.

Explanation:

Step1: Convert mixed numbers to improper fractions

The formula for the area of a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length, and \(w\) is the width.
Convert \(3\frac{7}{8}\) to an improper fraction: \(3\frac{7}{8}=\frac{3\times8 + 7}{8}=\frac{24+7}{8}=\frac{31}{8}\)
Convert \(6\frac{15}{16}\) to an improper fraction: \(6\frac{15}{16}=\frac{6\times16+15}{16}=\frac{96 + 15}{16}=\frac{111}{16}\)

Step2: Substitute into the area formula

Substitute \(A=\frac{111}{16}\) and \(l = \frac{31}{8}\) into \(A=l\times w\)
We get the equation \(\frac{111}{16}=\frac{31}{8}\times w\)

Answer:

\(\frac{111}{16}=\frac{31}{8}\times w\)