Question

How many rational numbers are between 1/3 and 1/4

Answer 1

The rational number between 1/4 and 1/3 is 7/24.

To find:

Rational number between 1/4 and 1/3

Solution:

When we want to find out rational number between two rational numbers, we have to take the arithmetic mean of those two numbers. Hence, if we want to find rational number between 1/4 and 1/3, we will have to calculate their arithmetic mean.

\begin{array} { c } { \left( \frac { 1 } { 2 } \right) \left( \frac { 1 } { 4 } + \frac { 1 } { 3 } \right) } \\\\ { = \left( \frac { 1 } { 2 } \right) \left( \frac { 3 } { 12 } + \frac { 4 } { 12 } \right) } \\\\ { = \left( \frac { 1 } { 2 } \right) \left( \frac { 7 } { 12 } \right) } \\\\ { = \frac { 7 } { 24 } } \end{array}

Hence, the rational number between 1/4 and 1/3 is 7/24.

Answer 2

There are many rational numbers between any two numbers which can not be defined.

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