Show that 37 lies between 25 and 57

37 will lie between 25 and 57 if 25 gt;37 gt;57 or 25 lt;37 lt;57 Now, comparing 25,37,57 L.C.M of 5 and 7 3 ...

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Question

Show that $\frac{3}{7}$ lies between $\frac{2}{5}$ and $\frac{5}{7}$

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Solution

$\frac{3}{7}$ will lie between $\frac{2}{5}$ and $\frac{5}{7}$ if
$\frac{2}{5} > \frac{3}{7} > \frac{5}{7}$ or $\frac{2}{5} < \frac{3}{7} < \frac{5}{7}$
Now, comparing $\frac{2}{5}, \frac{3}{7}, \frac{5}{7}$
L.C.M of $5$ and $7 - 35$
$∴ \frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}$
$\frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35}$
and $\frac{5}{7} = \frac{5 \times 5}{7 \times 5} = \frac{25}{35}$
$∴ \frac{14}{35} < \frac{15}{35} < \frac{25}{35}$
$\frac{2}{5} < \frac{3}{7} < \frac{5}{7}$
$∴ \frac{3}{7}$ lies between $\frac{2}{5}$ and $\frac{5}{7}$

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Show that 37 lies between 25 and 57

37 will lie between 25 and 57 if25>37>57 or 25<37<57Now, comparing 25,37,57L.C.M of 5 and 7−35∴25=2×75×7=143537=3×57×5=1535and 57=5×57×5=2535∴1435<1535<253525<37<57∴37 lies between 25 and 57

Show that $\frac{3}{7}$ lies between $\frac{2}{5}$ and $\frac{5}{7}$