Skill: Compare ratios

To compare two ratios, rewrite them so they use the same comparison basis. You can use equivalent ratios or find a unit rate.

Example: Which ratio is greater: $3:5$ or $4:7$?

Suppose these ratios describe red marbles to blue marbles:

• $3:5$ means 3 red marbles for every 5 blue marbles.
• $4:7$ means 4 red marbles for every 7 blue marbles.

Do not compare only the first numbers. Although $4$ is greater than $3$, the ratios have different second numbers. Instead, write the ratios as fractions:

$$\frac{3}{5} \quad \text{and} \quad \frac{4}{7}$$

Find a common denominator. The least common denominator of 5 and 7 is 35:

$$\frac{3}{5}=\frac{21}{35}$$

and

$$\frac{4}{7}=\frac{20}{35}$$

Now compare:

$$\frac{21}{35}>\frac{20}{35}$$

Therefore,

$$\boxed{3:5 \text{ is greater than } 4:7}$$

Both ratios now describe how many red marbles there are out of 35 blue-marble parts, so the comparison is fair.