# 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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