Question
$\text { Show that } \frac{4}{5} \text { lies between } \frac{3}{4} \text { and } \frac{5}{6} \text {. }$
✓
Answer
$\frac{3}{4}>\frac{4}{5}>\frac{5}{6} \text { or } \frac{3}{4}<\frac{4}{5}<\frac{5}{6}$
Now L.C.M. of $4, 5, 6=60$
$\therefore \frac{3}{4}=\frac{3 \times 15}{4 \times 15}=\frac{45}{60} $
$\frac{4}{5}=\frac{4 \times 12}{5 \times 12}=\frac{48}{60} $
$\frac{5}{6}=\frac{5 \times 10}{6 \times 10}=\frac{50}{60} $
$\therefore \frac{45}{60}<\frac{48}{60}<\frac{50}{60} $
$\Rightarrow \frac{3}{4}<\frac{4}{5}<\frac{5}{6}$
Hence $\frac{4}{5}$ lies between $\frac{3}{4}$ and $\frac{5}{6}$
Now L.C.M. of $4, 5, 6=60$
$\therefore \frac{3}{4}=\frac{3 \times 15}{4 \times 15}=\frac{45}{60} $
$\frac{4}{5}=\frac{4 \times 12}{5 \times 12}=\frac{48}{60} $
$\frac{5}{6}=\frac{5 \times 10}{6 \times 10}=\frac{50}{60} $
$\therefore \frac{45}{60}<\frac{48}{60}<\frac{50}{60} $
$\Rightarrow \frac{3}{4}<\frac{4}{5}<\frac{5}{6}$
Hence $\frac{4}{5}$ lies between $\frac{3}{4}$ and $\frac{5}{6}$
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