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Which of the following numbers is between the rational numbers $\frac{6}{10}$ and $\frac{5}{10}$ ?

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\frac{1}{4}

\frac{3}{4}

\frac{21}{40}

\frac{33}{100}

answer is C.

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Detailed Solution

The given fractions are

\frac{6}{10}

and

\frac{5}{10}

.
Multiplying the denominator and numerator by

4

\Rightarrow \frac{5}{10} \times \frac{4}{4} = \frac{20}{40}

\Rightarrow

\frac{6}{10} \times \frac{4}{4} = \frac{24}{40}

The numbers between the numerators 20 and 24 are 21, 22, 23.
In option 3, 21 is the numerator, which is one of the numbers between 20 and 24.
Thus, number between

\frac{20}{40}

and

\frac{24}{40}

\frac{21}{40} .

Hence, option 3 is correct.

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