Question

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Answer 1

Answer:

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answer and explanation is in attachment

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Answer 2

QUESTION:

❹ Find three rational numbers lying between $\bf{\dfrac {1}{5} \: and \: \dfrac {1}{4}}$

SOLUTION:

We have $\bf{\dfrac {1}{5} \: and \: \dfrac {1}{4}}$

L.C.M. of 5 and 4 = 20

∴ To make the denominators equal i.e., 20 we multiply numerator and denominator of $\bf{\dfrac {1}{5}}$ by 4 and that of $\bf{\dfrac {1}{4}}$ by 5, we get $\bf{\dfrac {4}{20} \: and \: \dfrac {5}{20}}$

☞ To insert three rational numbers, we multiply the numerators of both the fractions by such a number 2 or 3 or 4...... so that the difference between the numerators is at least 3.

On multiplying the numerators and denominators of both fractions by 4, we get

$\sf{\rightharpoonup \large\frac{4}{20} \times \frac{4}{4} = \frac{16}{80}}$

$\sf{\rightharpoonup \large\frac{5}{20} \times \frac{4}{4} = \frac{20}{80}}$

Hence, the required three rational numbers between $\bf{\dfrac {1}{5} \: and \: \dfrac {1}{4}}$ are:

$\Large\bf{\frac{17}{80} , \frac{18}{80} , \frac{19}{80}}$

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QUESTION:

❺ Find three rational numbers lying between $\bf{\dfrac {2}{5} \: and \: \dfrac {3}{4}}$

SOLUTION:

We have $\bf{\dfrac {2}{5} \: and \: \dfrac {3}{4}}$

L.C.M. of 5 and 4 = 20

∴ To make the denominators equal i.e., 20 we multiply numerator and denominator of $\bf{\dfrac {2}{5}}$ by 4 and that of $\bf{\dfrac {3}{4}}$ by 5

$\sf{\rightharpoonup \frac {2}{5} \times \frac {4}{4} = \frac{8}{20}}$

$\sf{\rightharpoonup \frac {3}{4} \times \frac {5}{5} = \frac{15}{20}}$

Thus, the required five rational numbers between $\bf{\dfrac {2}{5} \: and \: \dfrac {3}{4}}$ are:

$\Large\bf{\frac{9}{20} , \frac{10}{20} , \frac{11}{20} , \frac{12}{20} , \frac{13}{20}}$

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