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Hint: Comprehending two fractions is easier when the denominator is equal for both of them. Make the denominators of both the fractions equal by multiplying them with a factor, then consider the rational numbers to find the answer.

Complete step-by-step answer:

Numbers ⟶ $\dfrac{{ - 2}}{5}$ and $\dfrac{1}{2}$.

In order to make the denominators equal for both the fractions

For $\dfrac{{ - 2}}{5}$, multiply the factor ‘4’ on the numerator and denominator

⟹$\dfrac{{ - 2 \times 4}}{{5 \times 4}}$= $\dfrac{{ - 8}}{{20}}$

For $\dfrac{1}{2}$, multiply the factor ‘10’ on the numerator and denominator

⟹$\dfrac{{1 \times 10}}{{2 \times 10}}$=$\dfrac{{10}}{{20}}$

Therefore, ten rational numbers between $\dfrac{{ - 8}}{{20}}$ and $\dfrac{{10}}{{20}}$are$\dfrac{{ - 7}}{{20}},\dfrac{{ - 6}}{{20}},\dfrac{{ - 5}}{{20}},\dfrac{{ - 4}}{{20}},\dfrac{{ - 3}}{{20}},\dfrac{1}{{20}},\dfrac{2}{{20}},\dfrac{3}{{20}},\dfrac{4}{{20}},\dfrac{5}{{20}}$.

Note –

In such types of questions the key is to make the denominators of given fractions equal by multiplying them with suitable factors. The fractions can be multiplied with suitable factors multiple times in order to get the required number of rational numbers in between them. The ratio of the given fraction is not altered when multiplied with the same factor on both the numerator and the denominator.

Complete step-by-step answer:

Numbers ⟶ $\dfrac{{ - 2}}{5}$ and $\dfrac{1}{2}$.

In order to make the denominators equal for both the fractions

For $\dfrac{{ - 2}}{5}$, multiply the factor ‘4’ on the numerator and denominator

⟹$\dfrac{{ - 2 \times 4}}{{5 \times 4}}$= $\dfrac{{ - 8}}{{20}}$

For $\dfrac{1}{2}$, multiply the factor ‘10’ on the numerator and denominator

⟹$\dfrac{{1 \times 10}}{{2 \times 10}}$=$\dfrac{{10}}{{20}}$

Therefore, ten rational numbers between $\dfrac{{ - 8}}{{20}}$ and $\dfrac{{10}}{{20}}$are$\dfrac{{ - 7}}{{20}},\dfrac{{ - 6}}{{20}},\dfrac{{ - 5}}{{20}},\dfrac{{ - 4}}{{20}},\dfrac{{ - 3}}{{20}},\dfrac{1}{{20}},\dfrac{2}{{20}},\dfrac{3}{{20}},\dfrac{4}{{20}},\dfrac{5}{{20}}$.

Note –

In such types of questions the key is to make the denominators of given fractions equal by multiplying them with suitable factors. The fractions can be multiplied with suitable factors multiple times in order to get the required number of rational numbers in between them. The ratio of the given fraction is not altered when multiplied with the same factor on both the numerator and the denominator.

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