Find ten rational numbers between


Find ten rational numbers between $\frac{1}{4}$ and $\frac{1}{2}$.


The L.C.M of the denominators $(2$ and 4$)$ is 4 .

So, we can write $\frac{1}{4}$ as it is.

Also, $\frac{1}{2}=\frac{1 \times 2}{2 \times 2}=\frac{2}{4}$

As the integers between the numerators 1 and 2 of both the fractions are not sufficient, we will multiply the fractions by 20 .

$\therefore \frac{1}{4}=\frac{1 \times 20}{4 \times 20}=\frac{20}{80}$

$\frac{2}{4}=\frac{2 \times 20}{4 \times 20}=\frac{40}{80}$

Between 20 and 40, there are 19 integers. They are $21,22,23,24,25,26,27 \ldots \ldots 39,40 .$

Thus $, \frac{21}{40}, \frac{22}{40}, \frac{23}{40}, \frac{24}{40}, \frac{25}{40}, \ldots \ldots \ldots \ldots \ldots \ldots . \frac{38}{40}$ and $\frac{39}{40}$ are the fractions.

We can take any 10 of these.

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