write the ratio 12:36 as an equivalent ratio of x:3

Proportional relationships

1 answer

To find an equivalent ratio for \( 12:36 \) in the form of \( x:3 \), we can set up a proportion.

First, simplify the ratio \( 12:36 \):

\[ \frac{12}{36} = \frac{1}{3} \]

Now, we want to express \( x:3 \) as an equivalent ratio to \( \frac{1}{3} \):

\[ \frac{x}{3} = \frac{1}{3} \]

Now, we can cross-multiply to solve for \( x \):

\[ x \cdot 3 = 1 \cdot 3 \] \[ 3x = 1 \]

Now, divide both sides by 3:

\[ x = \frac{1}{3} \]

So, the equivalent ratio \( x:3 \) is:

\[ \frac{1/3}{3} = \frac{1}{3} : 3 \]

Thus, \( x = \frac{1}{3} \) gives you the ratio:

\[ \frac{1}{3} : 3 \]

In summary, for the ratio \( 12:36 \), the equivalent ratio in the form \( x:3 \) is:

\[ \frac{1}{3} : 3 \]