Question
Put the given fraction in ascending order by making denominator equal:
$\frac{5}{7}, \frac{3}{8}, \frac{9}{14} \text { and } \frac{20}{21}$
$\frac{5}{7}, \frac{3}{8}, \frac{9}{14} \text { and } \frac{20}{21}$
✓
Answer
$ \frac{5}{7}, \frac{3}{8}, \frac{9}{14} \text { and } \frac{20}{21} $
L.C.M. of denominators 7, 8, 14 and $21=168$
$ \begin{aligned} & \therefore \frac{5}{7}=\frac{5 \times 24}{7 \times 24}=\frac{120}{168} \\ & \frac{3}{8}=\frac{3 \times 21}{8 \times 21}=\frac{63}{168} \\ & \frac{9}{14}=\frac{9 \times 12}{14 \times 12}=\frac{108}{168} \\ & \frac{20}{21}=\frac{20 \times 8}{21 \times 8}=\frac{160}{168} \end{aligned} $
It is clear from the above that
$ \begin{aligned} & \frac{63}{168}<\frac{108}{168}<\frac{120}{168}<\frac{160}{168} \\ & \text { or } \frac{3}{8}<\frac{9}{14}<\frac{5}{7}<\frac{20}{21} \end{aligned} $
Hence, $\frac{3}{8}, \frac{9}{14}, \frac{5}{7}$ and $\frac{20}{21}$ are in ascending order.
L.C.M. of denominators 7, 8, 14 and $21=168$
$ \begin{aligned} & \therefore \frac{5}{7}=\frac{5 \times 24}{7 \times 24}=\frac{120}{168} \\ & \frac{3}{8}=\frac{3 \times 21}{8 \times 21}=\frac{63}{168} \\ & \frac{9}{14}=\frac{9 \times 12}{14 \times 12}=\frac{108}{168} \\ & \frac{20}{21}=\frac{20 \times 8}{21 \times 8}=\frac{160}{168} \end{aligned} $
It is clear from the above that
$ \begin{aligned} & \frac{63}{168}<\frac{108}{168}<\frac{120}{168}<\frac{160}{168} \\ & \text { or } \frac{3}{8}<\frac{9}{14}<\frac{5}{7}<\frac{20}{21} \end{aligned} $
Hence, $\frac{3}{8}, \frac{9}{14}, \frac{5}{7}$ and $\frac{20}{21}$ are in ascending order.
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