Question

The ratio $8:2$ and $16:.............$ are equivalent.

Answer 1

Definition:

Equivalent Ratios: The Ratio exists in one or more different forms but we get the same ratio after simplifying those different forms. So Equivalent ratios are equated.

ex: the equivalent ratio of $2:3$ is $4:6$, $8:12$. we get same $8:12$ after simplifying $4:6$and $8:12$.

Solution / Explanation :

It is given that the ratio $8:2$ and $16:.............$ are equivalent.

Let assume the blank is $\text{'}x\text{'}$.

So, $8:2$ and $16:x$ are equivalent.

Now, write in fraction form and equate them.

$\frac{8}{2}=\frac{16}{x}$ ( apply cross-multiplication )

$8\times x=16\times 2$

transpose $8$ to the RHS

$x=\frac{16\times 2}{8}$

on dividing $16by8$, we get

$$\begin{gathered} x=2\times 2 \\ x=4. \end{gathered}$$

So, The ratio $8:2$ and $16:4$ are equivalent.

Hence, the answer of the given blank is $4$.