Skill: Write ratios in multiple forms

A ratio compares two quantities in a specific order. The order must stay the same in every form.

Suppose a bag has 3 red marbles and 5 blue marbles. To write the ratio of red marbles to blue marbles:

1. Identify the order.
   Red comes first, so use $3$. Blue comes second, so use $5$.

2. Write the ratio in colon notation.

$$3:5$$

3. Write the ratio using the word “to.”

$$3\text{ to }5$$

4. Write the ratio as a fraction.

$$\frac{3}{5}$$

So, the ratio of red marbles to blue marbles can be written as

$$3:5=3\text{ to }5=\frac{3}{5}.$$

These forms have the same meaning. If the order changes, the meaning changes: the ratio of blue marbles to red marbles would be $5:3$, or $5\text{ to }3$, or $\frac{5}{3}$.