Question

1. for each figure below:

• write a multiplication expression to represent the area of the shaded re
• find the area of the shaded region, in square units, using any strategy.

a)

Explanation:

Step1: Determine the fraction of shaded columns and rows

The total number of columns is \(6\), and the number of shaded columns is \(5\). So the fraction of shaded columns is \(\frac{5}{6}\). The total number of rows is \(3\), and all rows are shaded. So the fraction of shaded rows is \(\frac{3}{3}=1\).

Step2: Write the multiplication expression

The area of a rectangle is length times width. Here, if we consider the fraction of shaded parts in terms of columns (width - like dimension) and rows (length - like dimension), the multiplication expression for the area of the shaded region is \(\frac{5}{6}\times1\).

Step3: Calculate the area

We know that when we multiply a fraction \(\frac{a}{b}\) by \(1\) (\(\frac{c}{c}\), where \(c = 3\) in our row - fraction case), \(\frac{5}{6}\times1=\frac{5\times1}{6\times1}\). The area of the whole rectangle (when considering each small square has area \(1\times1 = 1\) square unit and there are \(6\times3=18\) small squares in total) is \(1\times1\times6\times3 = 18\) square units. The number of shaded squares is \(5\times3 = 15\). So \(\frac{5}{6}\times1=\frac{5}{6}\) (since the area of the whole rectangle is \(6\) square units when we consider the unit length as \(1\) for the side of the big - rectangle. Another way: \(\frac{5}{6}\times1=\frac{5}{6}\) square units (if the area of the rectangle with sides \(1\) and \(1\) is \(1\) square unit, and we scale one side by \(\frac{5}{6}\)).

Answer:

• Multiplication expression: \(\frac{5}{6}\times1\)
• Area of the shaded region: \(\frac{5}{6}\) square units