MCQ
Which one of the following is the correct statement$?$
- A$\frac{3}{4}<\frac{2}{3}<\frac{12}{5}$
- ✓$\frac{2}{3}<\frac{3}{4}<\frac{12}{15}$
- C$\frac{2}{3}<\frac{12}{15}<\frac{3}{4}$
- D$\frac{12}{15}<\frac{2}{3}<\frac{3}{4}$
Consider the fractions $\frac{3}{4},\frac{2}{3}$ and $\frac{12}{15}$
$LCM$ of $4, 3$ and $15 = 60$
Firstly, convert the fractions into equivalent fractions with denominator $60$
$\Rightarrow\frac{3}{4}=\frac{3\times15}{4\times15}=\frac{45}{60}$
$\Rightarrow\frac{2}{3}=\frac{2\times20}{3\times20}=\frac{40}{60}$
$\Rightarrow\frac{12}{15}=\frac{12\times4}{15\times4}=\frac{48}{60}$
Now,
$40<45<48$
$\therefore\ \frac{40}{60}<\frac{45}{60}<\frac{48}{60}$
$\frac{2}{3}<\frac{3}{4}<\frac{12}{15}$
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