Question

the rectangle shown below represents 1 whole. click on pieces in the rectangle to shade $\frac{4}{5}$ of the rectangle.

Explanation:

Step1: Understand fraction meaning

The fraction $\frac{4}{5}$ means 4 parts out of 5 equal - sized parts.

Step2: Identify number of parts

The rectangle is divided into 9 equal - sized parts. We need to find an equivalent fraction with denominator 9. Let the number of shaded parts be $x$. We set up the proportion $\frac{4}{5}=\frac{x}{9}$. Cross - multiply: $5x = 4\times9=36$. Then $x=\frac{36}{5}=7.2$. But since we are dealing with whole parts, if we assume we want to shade as close as possible to $\frac{4}{5}$ of the rectangle, we can think of it in terms of a common - sense approach. If we consider the closest whole - number approximation, we know that $\frac{4}{5}=0.8$ and $0.8\times9 = 7.2\approx7$ (rounding down). Another way is to note that if we consider the fraction $\frac{4}{5}$ in terms of dividing the rectangle into 5 equal groups (even though it's divided into 9), we can shade 4 out of every 5 "virtual" groups. Since we have 9 parts, we shade 7 parts (because if we group them in sets of 5, we can make 1 full set of 5 and 4 remaining parts, and we shade 4 from the first set of 5 and 3 from the remaining 4 to get as close to $\frac{4}{5}$ as possible).

Answer:

Shade 7 parts of the rectangle.