Question

today we wrote expressions that represent the area of a rectangle with side lengths greater than 1. here are some expressions we could use to find the area of the shaded region in this rectangle: 2\frac{1}{4}\times2 or 18\times\frac{1}{4} or \frac{9}{4}\times2 or \frac{18}{4} or 9\times2\times\frac{1}{4} 1) for each figure below: - write a multiplication expression to represent the area of the shaded region. - find the area of the shaded region, in square units, using any strategy. a)

Explanation:

Step1: Determine the dimensions of the rectangle

The rectangle has a length of \(5\frac{1}{3}\) (since there are \(16\) small squares in the length direction and each small square has a side - length of \(\frac{1}{3}\), \(16\times\frac{1}{3}=\frac{16}{3}=5\frac{1}{3}\)) and a width of \(3\) (since there are \(9\) small squares in the width direction and each small square has a side - length of \(\frac{1}{3}\), \(9\times\frac{1}{3} = 3\)). But if we consider the unit square concept (assuming each small square has an area of \(\frac{1}{3}\times\frac{1}{3}=\frac{1}{9}\) square units, and there are \(14\) shaded small squares in each row and \(3\) rows).
Another way: The rectangle is divided into columns and rows. Let's assume the side - length of each small square is \(\frac{1}{3}\). The number of shaded columns: \(14\) (out of \(16\)) and \(3\) rows.
The multiplication expression for the area of the shaded region: \(\frac{14}{16}\times3\) (simplifying \(\frac{14}{16}=\frac{7}{8}\)), so the expression is \(\frac{7}{8}\times3\)

Step2: Calculate the area

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Answer:

The multiplication expression is \(\frac{7}{8}\times3\) and the area of the shaded region is \(\frac{21}{8}=2\frac{5}{8}\) square units.