Question: How can we calculate the shaded area?
5 equal-sized rectangles, each with 3 of 5 equal sections shaded.
Choose 2 answers:
A
$5 \times \dfrac{5}{3}$
B
$5 \times \dfrac{3}{5}$
C
$\dfrac{3}{5} + \dfrac{3}{5} + \dfrac{3}{5} + \dfrac{3}{5} + \dfrac{3}{5}$
1. **State the problem:** We have 5 equal-sized rectangles, each divided into 5 equal sections, with 3 of those sections shaded in each rectangle.
2. **Goal:** Calculate the total shaded area across all 5 rectangles.
3. **Understanding the problem:** Each rectangle has $5$ sections, and $3$ of these are shaded, so the shaded fraction of one rectangle is $\frac{3}{5}$.
4. **Method 1 (Multiplication):** Multiply the number of rectangles by the shaded fraction per rectangle:
$$5 \times \frac{3}{5}$$
5. **Method 2 (Addition):** Add the shaded fractions for each rectangle:
$$\frac{3}{5} + \frac{3}{5} + \frac{3}{5} + \frac{3}{5} + \frac{3}{5}$$
6. **Simplify the addition:**
$$\frac{3}{5} + \frac{3}{5} + \frac{3}{5} + \frac{3}{5} + \frac{3}{5} = 5 \times \frac{3}{5}$$
7. **Calculate the product:**
$$5 \times \frac{3}{5} = \cancel{5} \times \frac{3}{\cancel{5}} = 3$$
8. **Interpretation:** The total shaded area is $3$ whole sections.
9. **Check option A:** $5 \times \frac{5}{3}$ is incorrect because it implies more shaded area than total sections.
10. **Correct answers:** B and C represent the correct calculations for the shaded area.
**Final answer:** The total shaded area is $3$ sections.