Question
From the given pairs, find which ratio is larger: $(3 : 7)$ or $(4 : 9)$
✓
Answer
$(3 : 7)$ or $(4 : 9)$
$\Rightarrow\frac{3}{7},\frac{4}{9}$
$\text{LCM of }7,9=63$
$\therefore\frac{3}{7}=\frac{3\times9}{7\times9}=\frac{27}{63}$
$\frac{4}{9}=\frac{4\times7}{9\times7}=\frac{28}{63}$
We see that $\frac{28}{63}>\frac{27}{63}\text{ or }\frac{4}{9}>\frac{3}{7}$
$\therefore4:9$ is greater ratio.
$\Rightarrow\frac{3}{7},\frac{4}{9}$
$\text{LCM of }7,9=63$
$\therefore\frac{3}{7}=\frac{3\times9}{7\times9}=\frac{27}{63}$
$\frac{4}{9}=\frac{4\times7}{9\times7}=\frac{28}{63}$
We see that $\frac{28}{63}>\frac{27}{63}\text{ or }\frac{4}{9}>\frac{3}{7}$
$\therefore4:9$ is greater ratio.
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