Find three rational numbers between frac{2}{3 | vedclass

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Question

(A) To find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$,first make the denominators equal by finding the least common multiple $(LC

Vedclass · Accepted Answer

$\frac{21}{30}, \frac{22}{30}, \frac{23}{30}$

Vedclass · Answer

(A) To find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$,first make the denominators equal by finding the least common multiple $(LCM)$ of $3$ and $5$,which is $15$.Convert the fractions: $\frac{2}{3} = \frac{2 	imes 5}{3 	imes 5} = \frac{10}{15}$ and $\frac{4}{5} = \frac{4 	imes 3}{5 	imes 3} = \frac{12}{15}$.Since we need three numbers,multiply the numerator and denominator of both fractions by $(3 + 1) = 4$ (or any number greater than $3$).$\frac{10}{15} = \frac{10 	imes 4}{15 	imes 4} = \frac{40}{60}$ and $\frac{12}{15} = \frac{12 	imes 4}{15 	imes 4} = \frac{48}{60}$.Three rational numbers between $\frac{40}{60}$ and $\frac{48}{60}$ are $\frac{41}{60}, \frac{42}{60}, 	ext{and } \frac{43}{60}$.

Find three rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.

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