Question
Insert five rational numbers between $\frac{3}{5}$ and $\frac{2}{3}$
✓
Answer
$\text{LCM} $of denominators $5$ and $3$ is $15.$
make the denominator of each given rational number equal to $15$ i.e., the $\text{LCM}.$
$\frac{3}{5}=\frac{3 \times 3}{5 \times 3}=\frac{9}{15}$ and
Since five rational numbers are required, multiply the numerator and denominator of each rational number by $5+1=6$.
$\therefore \frac{9}{15}=\frac{9 \times 6}{15 \times 6}=\frac{54}{90}$ and
$\frac{10}{15}=\frac{10 \times 6}{15 \times 6}=\frac{60}{90}$
$\therefore$ Required rational numbers between $\frac{3}{5}$ and $\frac{2}{3}$ are $\frac{55}{90}, \frac{56}{90}, \frac{57}{90}, \frac{58}{90}$, and $\frac{59}{90}$.
$=\frac{11}{18}, \frac{28}{45}, \frac{19}{35}, \frac{29}{45}$ and $\frac{59}{90}$
make the denominator of each given rational number equal to $15$ i.e., the $\text{LCM}.$
$\frac{3}{5}=\frac{3 \times 3}{5 \times 3}=\frac{9}{15}$ and
Since five rational numbers are required, multiply the numerator and denominator of each rational number by $5+1=6$.
$\therefore \frac{9}{15}=\frac{9 \times 6}{15 \times 6}=\frac{54}{90}$ and
$\frac{10}{15}=\frac{10 \times 6}{15 \times 6}=\frac{60}{90}$
$\therefore$ Required rational numbers between $\frac{3}{5}$ and $\frac{2}{3}$ are $\frac{55}{90}, \frac{56}{90}, \frac{57}{90}, \frac{58}{90}$, and $\frac{59}{90}$.
$=\frac{11}{18}, \frac{28}{45}, \frac{19}{35}, \frac{29}{45}$ and $\frac{59}{90}$
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