MCQ
Which of the following is correct$?$
- ✓$\frac{5}{9}>\frac{-3}{8}$
- B$\frac{5}{9}<\frac{-3}{-8}$
- C$\frac{2}{-3}<\frac{-8}{7}$
- D$\frac{4}{-3}>\frac{-8}{7}$
Consider the rational numbers $\frac{5}{9}\text{ and } \frac{-3}{-8}$
We write the rational number $\frac{-3}{-8}$ with positive denominator.
$\frac{-3}{-8}=\frac{-3\times(-1)}{-8\times(-1)}=\frac{3}{8}$
Now, we write the rational numbers so that they have a common denominator.
$LCM$ of $8$ and $9 = 72$
So, $\frac{5}{9}=\frac{5\times8}{9\times8}=\frac{40}{72}$ and $\frac{3}{8}=\frac{3\times9}{8\times9}=\frac{27}{72}$
Now,
$40>27$
$\Rightarrow\frac{40}{72}>\frac{27}{72}$
$\Rightarrow\frac{5}{9}>\frac{3}{8}$
$\Rightarrow\frac{5}{9}>\frac{-3}{-8}$
Hence the correct option is $(a).$
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