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Q.

Which of the rational number is between $\frac{1}{4}$ and $\frac{1}{3}$ ?

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a

\frac{10}{20}

b

\frac{20}{48}

c

\frac{10}{30}

d

\frac{7}{24}

answer is D.

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Detailed Solution

To find the rational number between

\frac{1}{4}

and

\frac{1}{3}

.
We know that a rational number

n_{1}

can be find in between

a and b

such that

a < n_{1} < b

using the formula

n_{1} = \frac{a + b}{2}

.
Substitute

a = \frac{1}{4}, b = \frac{1}{3}

in the formula.

\Rightarrow n_{1} = \frac{\frac{1}{4} + \frac{1}{3}}{2}

By cross multiplying and solving, we get

\Rightarrow n_{1} = \frac{\frac{3 + 4}{12}}{2}

{\Rightarrow n}_{1} = \frac{7}{2 \times 12}

{\Rightarrow n}_{1} = \frac{7}{24}

From this, we can see

\frac{7}{24}

lies between

\frac{1}{4}

and

\frac{1}{3}

.
Therefore, option 4 is correct.

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