Question

Rational numbers between $\frac{3}{8}$ and $\frac{7}{12}$ are

• A. $\frac{3}{8},\frac{41}{96},\frac{23}{48},\frac{7}{12}$
• B. $\frac{3}{8},\frac{41}{196},\frac{23}{48},\frac{7}{12}$
• C. $\frac{3}{8},\frac{41}{96},\frac{23}{148},\frac{7}{12}$
• D. none of the above

Answer 1

The correct option is A $\frac{3}{8},\frac{41}{96},\frac{23}{48},\frac{7}{12}$

A rational number between two numbers $a$ and $b=\frac{(a+b)}{2}$
So, a rational number between $\frac{3}{8}$ and $\frac{7}{12}$

$=\frac{\frac{3}{8}+\frac{7}{12}}{2}=\frac{23}{48}$

Now, another rational number between $\frac{3}{8}$ and $\frac{23}{48}$

$=\frac{\frac{3}{8}+\frac{23}{48}}{2}=\frac{41}{96}$

Hence, required two rational numbers between $\frac{3}{8}$ and $\frac{7}{12}$ are $\frac{3}{8},\frac{41}{96},\frac{23}{48},\frac{7}{12}$