Question

Fill in the following blanks: $\frac{15}{18}=\frac{\boxed{}}{6}=\frac{10}{\boxed{}}=\frac{\boxed{}}{30}$. Are these equivalent ratios?

Answer 1

Step 1: Finding the first missing number

We have,

$\frac{15}{18}=\frac{\boxed{}}{6}=\frac{10}{\boxed{}}=\frac{\boxed{}}{30}$

In order to get the first missing number, we consider the fact that $18=6\times 3$, i.e. when we divide $18$ by $3$ we get $6$. This indicates that to get the missing number of the second ratio, $15$ must also be divided by $3$.

When we divide, we have, $15÷3=5$.

Hence, the second ratio is $\frac{5}{6}$.

Step 2: Finding the second missing number

Now we have,

$\frac{15}{18}=\frac{\boxed{5}}{6}=\frac{10}{\boxed{}}=\frac{\boxed{}}{30}$

In order to get the second missing number, we consider the fact that $5\times 2=10$, i.e. when we multiply $5$ by $2$ we get $10$. This indicates that to get the missing number of the third ratio, $6$ must also be multiplied by $2$.

When we multiply, we have, $6\times 2=12$.

Hence, the third ratio is $\frac{10}{12}$.

Step 3: Finding the third missing number

Now we have,

$\frac{15}{18}=\frac{\boxed{5}}{6}=\frac{10}{\boxed{12}}=\frac{\boxed{}}{30}$

Consider, second and fourth ratio i.e. $\frac{\boxed{5}}{6}=\frac{\boxed{}}{30}$

In order to get the missing number, we consider the fact that $6\times 5=30$, i.e. when we multiply $6$ by $5$ we get $30$. This indicates that to get the missing number,$5$ must also be multiplied by $5$.

When we multiply, we have, $5\times 5=25$

Hence, the fourth ratio is $\frac{25}{30}$.

Thus, $\frac{15}{18}=\frac{\boxed{5}}{6}=\frac{10}{\boxed{12}}=\frac{\boxed{25}}{30}$. These are all equivalent ratios.