Question
Write the given rational numbers in ascending order.$\frac{-1}{3}, \frac{-2}{9}, \frac{-4}{3}$
✓
Answer
Firstly we need to make the denominators the same.
$\therefore$ taking the $LCM$ of $3, 9 \& 3$ we have $9$ as the $LCM$
Thus,
$\frac{-1}{3}=\frac{-1 \times 3}{3 \times 3}=\frac{-3}{9}. . . .[LCM (3, 9, 3) = 9]$
$\frac{-2}{9}=\frac{-2}{9}$
$\frac{-4}{3}=\frac{-4 \times 3}{3 \times 3}=\frac{-12}{9}$
$\because \frac{-12}{9}<\frac{-3}{9}<\frac{-2}{9}$
$\therefore \frac{-4}{3}<\frac{-1}{3}<\frac{-2}{9}$
$\therefore$ taking the $LCM$ of $3, 9 \& 3$ we have $9$ as the $LCM$
Thus,
$\frac{-1}{3}=\frac{-1 \times 3}{3 \times 3}=\frac{-3}{9}. . . .[LCM (3, 9, 3) = 9]$
$\frac{-2}{9}=\frac{-2}{9}$
$\frac{-4}{3}=\frac{-4 \times 3}{3 \times 3}=\frac{-12}{9}$
$\because \frac{-12}{9}<\frac{-3}{9}<\frac{-2}{9}$
$\therefore \frac{-4}{3}<\frac{-1}{3}<\frac{-2}{9}$
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