Question

Pick out the equivalent ratios from each of the following groups:

$12:24,16:30,11:23,18:36$

Answer 1

To find equivalent ratios from given ratios :

Let us write given ratio into fraction .

$12:24=\frac{12}{24}$

$16:30=\frac{16}{30}$

$11:23=\frac{11}{23}$

$18:36=\frac{18}{36}$

Now, we have to find the common factors that divide the numerator and denominator evenly and hence we get the simplified form of fractions.

$12:24=\frac{12}{24}=\frac{12÷12}{24÷12}=\frac{1}{2}$

$16:30=\frac{16}{30}=\frac{16÷2}{30÷2}=\frac{8}{15}$

$11:23=\frac{11}{23}$ ( They have no common factor other than one )

$18:36=\frac{18}{36}=\frac{18÷18}{36÷18}=\frac{1}{2}$

Thus, we can see all the fractions $\frac{12}{24}$ and $\frac{18}{36}$ are equivalent since their simplified forms are the same.

Therefore, the ratios $12:24$ and $18:36$ are also equivalent to each other.