Question
Which is greater in $\frac{2}{3}, \frac{5}{2}$
✓
Answer
We need to make the denominators of $3\ \&\ 2$ to common denominators. Thus we find the $LCM$ of $2\ \& \ 3$
$\frac{2}{3}=\frac{2 \times 2}{3 \times 2}=\frac{4}{6} . . . [LCM (3, 2) = 6]$
$\frac{5}{2}=\frac{5 \times 3}{2 \times 3}=\frac{15}{6}$
$\because$$\frac{15}{6}>\frac{4}{6}$ $\therefore$ $\frac{5}{2}>\frac{2}{3}$
Or
$2\over 3$ and $5\over 2$
cross multiplying the numerators we have
$2\times2$ and $5\times3$
$4$ and $15$
$\because 4< 15$
$\therefore$ $2\over 3$<$5\over 2$
$\frac{2}{3}=\frac{2 \times 2}{3 \times 2}=\frac{4}{6} . . . [LCM (3, 2) = 6]$
$\frac{5}{2}=\frac{5 \times 3}{2 \times 3}=\frac{15}{6}$
$\because$$\frac{15}{6}>\frac{4}{6}$ $\therefore$ $\frac{5}{2}>\frac{2}{3}$
Or
$2\over 3$ and $5\over 2$
cross multiplying the numerators we have
$2\times2$ and $5\times3$
$4$ and $15$
$\because 4< 15$
$\therefore$ $2\over 3$<$5\over 2$
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