Question: How can we calculate the shaded area?
3 equal-sized rectangles, each with 1 of 4 equal sections shaded.
Choose 2 answers:
A
$3 \times \dfrac{1}{4}$
B
$\dfrac{1}{4} + \dfrac{1}{4} + \dfrac{1}{4}$
C
$4 \times \dfrac{1}{3}$
1. **Problem statement:** We have 3 equal-sized rectangles, each divided into 4 equal sections, with 1 section shaded in each rectangle. We want to find the total shaded area.
2. **Understanding the problem:** Each rectangle has $4$ equal parts, and $1$ part is shaded. So the shaded area in one rectangle is $\frac{1}{4}$ of that rectangle.
3. **Method A:** Multiply the number of rectangles by the shaded fraction per rectangle:
$$3 \times \frac{1}{4}$$
This gives the total shaded area across all 3 rectangles.
4. **Method B:** Add the shaded fractions from each rectangle:
$$\frac{1}{4} + \frac{1}{4} + \frac{1}{4}$$
This sum also represents the total shaded area.
5. **Method C:** Multiply $4$ by $\frac{1}{3}$:
$$4 \times \frac{1}{3}$$
This does not represent the shaded area correctly because the rectangles are divided into 4 parts, not 3.
6. **Conclusion:** The correct ways to calculate the shaded area are methods A and B.
7. **Final answer:** The total shaded area is
$$3 \times \frac{1}{4} = \frac{3}{4}$$
or equivalently
$$\frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{3}{4}$$
which means $\frac{3}{4}$ of the total area of the 3 rectangles is shaded.