Lesson 3: Compare Ratios

Property

To compare two ratios, $A:B$ and $C:D$, create a ratio table for each.
Find equivalent ratios $A':B'$ and $C':D'$ such that one pair of corresponding terms is equal (e.g., $A' = C'$).
Then, compare the other pair of terms ($B'$ and $D'$) to determine which ratio is greater.

Examples

Property

To compare the total quantities represented by two ratios, first scale one or both ratios to find equivalent ratios with a common term. Then, sum the parts of each new equivalent ratio. The ratio with the larger sum corresponds to the greater total quantity.

Examples

• Two paint mixtures have a red to blue pigment ratio of $2:5$ and $3:7$ respectively. To compare which mixture has more paint for the same amount of red, we find a common term for red. The LCM of $2$ and $3$ is $6$. The first ratio becomes $6:15$ (total $21$) and the second becomes $6:14$ (total $20$). The first mixture has a greater total quantity ($21 > 20$).
• A class has a boy-to-girl ratio of $3:4$, and another class has a ratio of $1:2$. To compare totals based on the number of boys, we scale the second ratio. The first ratio is $3:4$ (total $7$). The second ratio becomes $3:6$ (total $9$). The second class is larger when there are $3$ boys in each.

Explanation

This skill extends ratio comparison to determine which situation represents a larger overall amount. By finding equivalent ratios with a common reference point, you can calculate the total for each scenario. You sum the two parts of the scaled ratio to find its total. Comparing these totals allows you to make decisions, such as determining which recipe yields more, or which group is larger.