# Word Problems Involving Comparing Ratio

Comparing ratios is the process of determining which ratio has a greater or smaller relationship between its terms.

In other words, it is the process of determining which ratio represents a larger or smaller quantity of something.

For example, if we have two ratios, such as 2:4 and 3:6, we can compare them to see which one represents a larger quantity. In this case, we can see that the ratio 2:4 represents half the quantity of the ratio 3:6 because 3 is 50% greater than 2, and 6 is 50% greater than 4.

There are two different methods to compare ratios: the LCM method and the cross-multiplication method.

Compare ratios with the LCM method which has three steps:

Step 1: Find the least common multiple (LCM) of the consequent.

Step 2: Divide it by the consequences.

Step 3: Multiply the quotient with the ratios.

To compare ratios with cross multiplication method, you have to follow this rule:

The antecedent of the first ratio × the consequent of the second ratio

and

the consequent of the first ratio × antecedent of the second ratio

**Word Problems Involving Comparing Ratio – Examples 1**

Oliver and David went bike riding every weekend. Oliver rode 5 miles in 1.5 hours and David rode 9 miles in 3 hours. Did Oliver and David go the same ratio of bike riding?**Solution:****Step 1: **The ratio of bike riding to hours for Oliver is \(\frac{5}{1.5}\). The ratio of bike riding to hours for David is \(\frac{9}{3}\).**Step 2: **Use cross multiplication. \(\frac{5}{1.5}=\frac{9}{3}→5×3=9×1.5→15≠13.5\)

So, Oliver and David didn’t ride the same ratio of the bike to hours.

**Word Problems Involving Comparing Ratio – Examples 2**

Jessi and Meg want to make a smoothie. Jessi made her smoothie with 3 cups of banana and 4 cups of strawberries. Meg made her smoothie with 6 cups of banana and 8 cups of strawberries. Did the smoothies have the same ratio of banana to strawberry?**Solution:****Step 1:** The ratio of banana to strawberry for Jessi is \(\frac{3}{4}\). The ratio of banana to strawberry for Meg is \(\frac{6}{8}\).**Step 2:** Simplify 6/8 to 3/4. The ratios are equal.

\(\frac{6}{8}=\frac{6÷2}{8÷2}=\frac{3}{4}\)

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