Question

# A rational number between $\frac{1}{4}$ and $\frac{1}{3}$ is

A

$\frac{16}{48}$

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B

$\frac{13}{48}$

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C

$\frac{7}{24}$

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D

All of the above

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Solution

## The correct option is C $\frac{7}{24}$Explanation for correct options:We have: $\frac{1}{4}$ and $\frac{1}{3}$The rational numbers equivalent to $\frac{1}{4}$ is $\frac{1×6}{4×6}=\frac{6}{24},\frac{1×12}{4×12}=\frac{12}{48}$The rational numbers equivalent to $\frac{1}{3}$is $\frac{1×8}{3×8}=\frac{8}{24},\frac{1×16}{3×16}=\frac{16}{48}$So,The rational numbers between $\frac{6}{24}$and$\frac{8}{24}$ is $\frac{7}{24}$The rational numbers between $\frac{12}{48}$and $\frac{16}{48}$are$\frac{13}{48},\frac{14}{48},\frac{15}{48}$Thus, the rational numbers between $\frac{1}{4}$ and $\frac{1}{3}$ are $\frac{7}{24},$$\frac{13}{48},\frac{14}{48},\frac{15}{48}$Hence, options (b) and (c) are correct.

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