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Which of the following is a proper fraction?

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(a)

(b)

(c)

All of the above

answer is D.

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Detailed Solution

Given figures are,
Question Image

Fraction is improper if the numerator is greater than or equal to the denominator.
In figure (a), rectangular object, there are a total of

8

squares and

4

of them are shaded, therefore, the fraction will be as follows.

\frac{Shaded}{Total} = \frac{4}{8} = \frac{1}{2} = 0.5 < 1

.
Hence,

\frac{1}{2}

is a proper fraction because the numerator is less than the denominator and the fraction is less than

1

In figure (b), rectangular object, there are a total of

9

squares and

6

of them are shaded, therefore, the fraction will be as follows.

\frac{Shaded}{Total} = \frac{6}{9} = \frac{2}{3} = 0.66 < 1

.
Hence,

\frac{2}{3}

is a proper fraction because the numerator is less than the denominator and the fraction is less than

1 .

In figure (c), triangular object, there are a total of

4

triangles and

1

of them is shaded, therefore, the fraction will be as follows.

\frac{Shaded}{Total} = \frac{1}{4} = 0.25 < 1

.
Hence,

\frac{1}{4}

is a proper fraction because the numerator is less than the denominator and the fraction is less than

1 .

The result is that all the given options are proper fractions.
Therefore, option (4) is correct.

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