Question

Which of the following diagrams shows $2 \times \dfrac{1}{5}$ ?
A.

B.

C.

D.

Answer 1

Hint: We will analyse each of the given options to determine if they constitute $2 \times \dfrac{1}{5}$ since $2 \times \dfrac{1}{5}$ represents a combination of two things (identical) which individually constitutes $\dfrac{1}{5}th$ of the total. We will check if each of the given figures in the individual option represents $\dfrac{1}{5}th$ of the total figure i.e., if the shaded portion is $\dfrac{1}{5}th$ of total figure.

Complete step-by-step answer:
A.

Here, we can see that there are 3 figures in total. And the shaded portion constitutes a total $\dfrac{4}{5}th$ of the circle. So, this can be represented as $3 \times \dfrac{4}{5}$ since there are 3 circles and each of them is $\dfrac{4}{5}th$ of the circle.
Therefore, option (A) is incorrect.
B.

In this diagram, we can see that there are 2 figures and they are equally divided in two parts. The shaded portion is half of the given rectangle i.e. the shaded portion is $\dfrac{1}{2}$ of the rectangle.
This can be represented as $2 \times \dfrac{1}{2}$ since there are two rectangles and each of them is shaded half.
Therefore, option (B) is incorrect.
C.

Here, we can see there are 3 figures given and each of them is divided into 4 equal squares and one of the square is shaded in each of them i.e., the shaded portion is $\dfrac{1}{4}th$ of each figure. We can represent this as $3 \times \dfrac{1}{4}$ because there are 3 figures and each of them has $\dfrac{1}{4}th$ shaded portion of the total.
Therefore, Option (C) is also incorrect.

D.

In this option, we can see there are 2 circles and they are equally divided into 5 sectors. Only one out of five sectors is shaded. So, we can say that the shaded portion is $\dfrac{1}{5}th$ of the total circle.
Hence, the figures can be represented as $2 \times \dfrac{1}{5}$ since there are 2 circles and each of them has $\dfrac{1}{5}th$ portion shaded.
Therefore, option (D) is correct.

Note: In this question, the only confusing part is the interpretation of $2 \times \dfrac{1}{5}$ as it represents a figure which has a total of two identical shapes and each of those must have a total of $\dfrac{1}{5}th$ portion shaded. In such questions, you can easily identify the correct answer by observation only but there can be more than one correct answer hence it is important to solve each option in order to avoid any error.