Compare ratios: word problems

Key notes :

Understanding Ratios: A ratio compares two quantities. It can be expressed in three ways:

  • Fraction form: a/b
  • Colon form: a:b
  • Word form: “a to b”

Simplifying Ratios: Ratios can often be simplified by dividing both terms by their greatest common factor (GCF). For example, 6:9 can be simplified to 2:3 by dividing both terms by 3.

Comparing Ratios: To compare two ratios, they must be expressed in the same form. This can involve:

  • Simplifying the ratios
  • Converting to equivalent ratios
  • Using cross-multiplication to compare ratios in fraction form.

Scaling Ratios: To make two ratios equivalent, multiply or divide each term of the ratio by the same number.

Learn with an example

✈️ A restaurant critic reviewed restaurants in Weston and Bluepoint. In Weston, the critic gave 20 positive reviews and 12 negative reviews. In Bluepoint, 12 of the reviews were positive and 11 were negative. In which city did the restaurant critic give a lower ratio of positive to negative reviews?

  • Weston
  • Bluepoint
  • neither; the ratios are equivalent
  • The ratio of positive to negative reviews by the restaurant critic for Weston was 20 to 12. The ratio for Bluepoint was 12 to 11.
  • We want to figure out which ratio is higher: 20/12 or 12/11
  • We can compare the ratios more easily if we express them as percentages.
  • First, write the ratio 20/12 as a decimal. Then convert the decimal to a percentage.
  • 20/12 ≈ 1.66667 = 166.667%
  • Do the same thing for 12/11
  • 12/11 ≈ 1.09091  = 109.091%
  • Now compare the percentages.
  • 166.667%? 109.091%
  • 109.091% is smaller than 166.667%.
  • The restaurant critic gave a lower ratio of positive to negative reviews in Bluepoint.

✈️ A pet supply chain called Pet City has 6 hamsters and 15 gerbils for sale at its Salem location. At its Richmond location, there are 5 hamsters and 14 gerbils. Which location has a higher ratio of hamsters to gerbils?

  • Salem
  • Richmond
  • neither; the ratios are equivalent
  • At the Salem location, the ratio of hamsters to gerbils is 6 to 15. At the Richmond location, the ratio is 5 to 14.
  • We want to figure out which ratio is higher: 6/15 or 5/14
  • We can compare the ratios more easily if we express them as percentages.
  • First, write the ratio 6/15 as a decimal. Then convert the decimal to a percentage.
  • 6/15 = 0.4 = 40%
  • Do the same thing for 5/14
  • 5/14 ≈ 0.35714 = 35.714%
  • Now compare the percentages.
  • 40% ? 35.714%
  • 40% is larger than 35.714%.
  • The Salem location has a higher ratio of hamsters to gerbils.

✈️ Last season, Bella’s soccer team won 12 games and lost 18 games. His cousin Erica’s team won 7 games and lost 14 games. Which team had a higher ratio of wins to losses?

  • Bella’s team
  • Erica’s team
  • neither; the ratios are equivalent
  • Last season, the ratio of wins to losses for Bella’s team was 12 to 18. The ratio for Erica’s team was 7 to 14.
  • We want to figure out which ratio is higher: 12/18 or 7/14
  • We can compare the ratios more easily if we express them as percentages.
  • First, write the ratio 12/18 as a decimal. Then convert the decimal to a percentage.
  • 12/18 ≈ 0.66667 = 66.667%
  • Do the same thing for 7/14
  • 7/14 = 0.5 = 50%
  • Now compare the percentages.
  • 66.667%? 50%
  • 66.667% is larger than 50%.
  • Bella’s team had a higher ratio of wins to losses.

Let’s practice! 🖊️