Question

Match the ratios on the left to their most simplified forms.

• A. $3:5$
• B. $2:3$
• C. $3:2$
• D. $1:21$

Answer 1

Note that the HCF of 12 and 20 is 4. If we now divide the antecedent and the consequent of the given ratio by 4, we get the simplest form of the ratio.
$⟹\frac{12}{4}:\frac{20}{4}=\frac{3}{1}:\frac{5}{1}=3:5$
Similarly, the HCF of 10 and 15 is 5.
$⟹\frac{10}{5}:\frac{15}{5}=\frac{2}{1}:\frac{3}{1}=2:3$,and therefore the simplest form of the given ratio is $2:3$.
Also, the HCF of 4 and 84 is 4.
$⟹\frac{4}{4}:\frac{84}{4}=\frac{1}{1}:\frac{21}{1}=1:21$
Now, consider the ratio $\frac{1}{2}:\frac{1}{3}$
The LCM of the denominator is 6. Multiply both $\frac{1}{2}$ and $\frac{1}{3}$ by 6.
$⟹\frac{1}{2}\times 6:\frac{1}{3}\times 6=3:2$