are rational numbers between 1-3 and 1-4

The correct option is B 1/3, 7/24, 13/48, 1/4 Arational number between two numbers a and b = (a +b)/2 So, arational number between 1/3 a ...

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Standard VIII

Mathematics

Rational Numbers between Two Rational Numbers

are rational ...

Question

________ are rational numbers between $\frac{1}{3}$ and $\frac{1}{4}$

\frac{1}{3}, \frac{7}{64}, \frac{13}{48}, \frac{1}{4}

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\frac{1}{3}, \frac{7}{24}, \frac{13}{48}, \frac{1}{4}

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\frac{1}{3}, \frac{7}{24}, \frac{13}{68}, \frac{1}{4}

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none of the above

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Solution

The correct option is B $\frac{1}{3}, \frac{7}{24}, \frac{13}{48}, \frac{1}{4}$
A
rational number between two numbers $a$ and $b = \frac{(a + b)}{2}$
So, a
rational number between $\frac{1}{3}$ and $\frac{1}{4} = \frac{(\frac{1}{3} + \frac{1}{4})}{2} = \frac{7}{24}$
Now, another rational number between $\frac{7}{24}$ and $\frac{1}{4} = \frac{(\frac{7}{24} + \frac{1}{4})}{2} = \frac{13}{48}$
Hence, required two rational numbers between $\frac{1}{3}$ and $\frac{1}{4}$ are $\frac{1}{3}, \frac{7}{24}, \frac{13}{48}, \frac{1}{4}$

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________ are rational numbers between 13 and 14

The correct option is B 13,724,1348,14Arational number between two numbers a and b=(a+b)2 So, arational number between 13 and 14=(13+14)2=724Now, another rational number between 724 and 14=(724+14)2=1348 Hence, required two rational numbers between 13 and 14 are 13,724,1348,14

________ are rational numbers between $\frac{1}{3}$ and $\frac{1}{4}$