Question
Compare the fractions given below: $\frac{11}{12},\frac{13}{15}$
✓
Answer
$L.C.M.$ of $12$ and $15 = (2 \times 2 \times 3 \times 5) = 60$
Now, we convert $\frac{11}{12}$ and $\frac{13}{15}$ into equivalent fractions having $40$ as the denominator.
$\therefore\frac{11}{12}=\frac{11\times5}{12\times5}=\frac{55}{60}$ and
$\frac{13}{15}=\frac{13\times4}{15\times4}=\frac{52}{60}$
Clearly, $\frac{55}{60}>\frac{52}{60}$
$\therefore\frac{11}{12}>\frac{13}{15}$
Now, we convert $\frac{11}{12}$ and $\frac{13}{15}$ into equivalent fractions having $40$ as the denominator.
$\therefore\frac{11}{12}=\frac{11\times5}{12\times5}=\frac{55}{60}$ and
$\frac{13}{15}=\frac{13\times4}{15\times4}=\frac{52}{60}$
Clearly, $\frac{55}{60}>\frac{52}{60}$
$\therefore\frac{11}{12}>\frac{13}{15}$
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