Question

This rectangle is divided into equal parts. Shanti says the shaded part is of the

area of the whole rectangle. Is Shanti correct?
Use the drop-down menus to explain your answer.

Answer 1

The whole rectangle has 4 equal parts and 1 is shaded. Shanti is not correct. One-fourth of the area of the whole rectangle is shaded.

The whole rectangle has 4 equal parts, and 1 part is shaded. Shanti is correct if the shaded area represents
`\((1)/(3)\)` of the entire rectangle's area. In this case, since there are four equal parts and only one is shaded, the ratio of the shaded area to the total area is
`\((1)/(4)\)`, not
`\((1)/(3)\)` as Shanti claimed.

Thus, Shanti is not correct. The shaded area is
`\((1)/(4)\)` of the total area, not
`\((1)/(3)\`) as stated. For Shanti's statement to be accurate, one-third of the rectangle should be shaded, which would correspond to having three equal parts shaded out of a total of nine.

In summary, Shanti's statement is incorrect because the actual ratio of the shaded area to the total area is
`\((1)/(4)\)`, not
`\((1)/(3)\)` as she claimed.