A rational number between 34 and 43 rational number is ____.

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A rational number between $\frac{3}{4} and \frac{4}{3}$ rational number is ____.

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Detailed Solution

According to the problem, we need to find a rational number between the following rational numbers
Now, let us find the rational that lies between the rational numbers

\frac{3}{4} and \frac{4}{3}

. We know that the average of the two numbers a and b lies between them and its value is

\frac{a + b}{2}

.
So, let us find the average of the rational numbers

\frac{3}{4} and \frac{4}{3}

. Let us assume that average as r1.

\Rightarrow r 1 = \frac{\frac{3}{4} + \frac{4}{3}}{2}

\Rightarrow r 1 = \frac{\frac{9 + 16}{12}}{2} .

\Rightarrow r 1 = \frac{\frac{25}{12}}{2} .

\Rightarrow r 1 = \frac{25}{24} .

∴ The rational numbers that lie between the rational numbers

\frac{3}{4} and \frac{4}{3}

\frac{25}{24}

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