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Find five rational numbers between $\dfrac{3}{5}{\text{ and }}\dfrac{4}{5}.$

Last updated date: 27th Mar 2023
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Hint- As we know that rational numbers are represented as $\dfrac{{\text{p}}}{q}$ . And we have to find more rational numbers between $\dfrac{3}{5}{\text{ and }}\dfrac{4}{5}.$ So, we multiply the numerator and denominator by the same number.

Given numbers are $\dfrac{3}{5}{\text{ and }}\dfrac{4}{5}.$
So, we have to find five numbers, we will multiply the given numbers by $\dfrac{6}{6}$
Let the number ${\text{A = }}\dfrac{3}{5}{\text{ and B = }}\dfrac{4}{5}$
Now, multiply A by $\dfrac{6}{6}$ , we obtain
${\text{A = }}\dfrac{3}{5} \times \dfrac{6}{6} = \dfrac{{18}}{{30}}$
And, multiply B by $\dfrac{6}{6}$ , we obtain
${\text{B = }}\dfrac{4}{5} \times \dfrac{6}{6} = \dfrac{{24}}{{30}}$
So, between $\dfrac{{18}}{{30}}{\text{ and }}\dfrac{{24}}{{30}}$ , we have to find rational numbers
Here, $\dfrac{{18}}{{30}} > \dfrac{{19}}{{30}} > \dfrac{{20}}{{30}} > \dfrac{{21}}{{30}} > \dfrac{{22}}{{30}} > \dfrac{{23}}{{30}} > \dfrac{{24}}{{30}}$
Hence five rational numbers between ${\text{A = }}\dfrac{3}{5}{\text{ and B = }}\dfrac{4}{5}$ are
$\dfrac{{19}}{{30}},\dfrac{{20}}{{30}},\dfrac{{21}}{{30}},\dfrac{{22}}{{30}},\dfrac{{23}}{{30}}$