Question

insert 4 rational numbers between 2/3 and 5/7​

Answer 1

Answer:

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Insert 4 rational numbers between $\sf \frac{2}{3}$ and $\sf \frac{5}{7}$

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$\large\sf{ \underline{To \: find : }}$

4 rational numbers between $\sf \frac{2}{3}$ and $\sf \frac{5}{7}$

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Equalise the denominators of these two rational numbers.

LCM of denominators = 3 × 7 = 21

∴ 21 is the common denominator.

Now,

$\large \sf \frac{2 \times 7}{3 \times 7} = \frac{14}{21}$

$\large \sf \frac{5 \times 3}{7 \times 3} = \frac{15}{21}$

Multiply both the rational numbers by 5.

$\large \sf \frac{14 \times 5}{21 \times 5} = \frac{70}{105}$

$\large \sf \frac{15 \times 5}{21 \times 5} = \frac{75}{105}$

4 Rational numbers between $\large \sf\frac{75}{105}$ or $\large \sf\frac{2}{3}$ and $\large \sf\frac{75}{105}$ or $\large \sf\frac{5}{7}$ are :

$\large \sf \frac{71}{105} , \frac{72}{105} , \frac{73}{105}, \frac{74}{105}$

$\sf \: Glad \: to \: help \: you...$

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