Which of the following is correct? - Vidyadip

MCQ

Which of the following is correct$?$

A
$\frac{2}{3}<\frac{3}{5}<\frac{11}{5}$
✓
$\frac{3}{5}<\frac{2}{3}<\frac{11}{15}$
C
$\frac{11}{15}<\frac{3}{5}<\frac{2}{3}$
D
$\frac{3}{5}<\frac{11}{15}<\frac{2}{3}$

✓

Answer

Correct option: B.

$\frac{3}{5}<\frac{2}{3}<\frac{11}{15}$

Consider the fractions $\frac{2}{3},\frac{3}{5}$ and $\frac{11}{15}$
$LCM$ of $3, 5$ and $15 = 15$
Firstly, convert the fractions into equivalent fractions with denominator $15$
$\Rightarrow\frac{2}{3}=\frac{2\times5}{3\times5}=\frac{10}{15}$
$\Rightarrow\frac{3}{5}=\frac{3\times3}{5\times3}=\frac{9}{15}$
Now,
$9<10<11$
$\therefore\ \frac{9}{15}<\frac{10}{15}<\frac{11}{15}$
$\frac{3}{5}<\frac{2}{3}<\frac{11}{15}$

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