Compare ratios: word problems

Key Notes :

  1. Understanding Ratios: Students should grasp the concept of ratios as relationships between two quantities. For instance, if there are 3 red marbles for every 5 blue marbles, the ratio of red marbles to blue marbles is 3:5.
  2. Real-Life Applications: Encourage students to apply ratios to various everyday scenarios. For example, they might consider ratios when baking (like a recipe calling for a certain ratio of flour to sugar), in financial contexts (like comparing the cost of items), or in sports (such as comparing the ratio of wins to losses in a team’s games).
  3. Solving Word Problems: Students should be proficient in interpreting and solving word problems that involve ratios. These problems may involve finding unknown quantities, comparing different ratios, or using ratios to solve for a particular outcome.
  4. Scale and Proportion: Understanding how ratios relate to scale and proportion is also vital. Students should comprehend how a change in one part of a ratio affects the other part and how these relationships can be represented visually, such as on a number line or in a bar model.
  5. Using Ratios for Comparison: The primary goal is for students to learn how to compare ratios effectively. They should understand the strategies to determine which ratio is greater or smaller and how to interpret these comparisons in practical situations.

Learn with an example

✈️ A restaurant critic reviewed restaurants in Lowell and Morristown. In Lowell, the critic gave 18 positive reviews and 12 negative reviews. In Morristown, 19 of the reviews were positive and 13 were negative.

In which city did the restaurant critic give a higher ratio of positive to negative reviews?

  • Lowell
  • Morristown
  • neither; the ratios are equivalent

The ratio of positive to negative reviews by the restaurant critic for Lowell was 18 to 12. The ratio for Morristown was 19 to 13.

We want to figure out which ratio is higher: 18/12 or 19/13 .

We can compare the ratios more easily if we express them as percentages.

First write the ratio 18/12 as a decimal. Then convert the decimal to a percentage.

18/12 = 1.5 = 150%

Do the same thing for 19/13 .

19/13 ≈ 1.46154 = 146.154%

Now compare the percentages.

150% ? 146.154%

150% is larger than 146.154%.

The restaurant critic gave a higher ratio of positive to negative reviews in Lowell.

✈️ Last season, Emily’s soccer team won 6 games and lost 8 games. His cousin Amy’s team won 11 games and lost 20 games.

Which team had a higher ratio of wins to losses?

  • Emily’s team
  • Amy’s team
  • neither; the ratios are equivalent

Last season, the ratio of wins to losses for Emily’s team was 6 to 8. The ratio for Amy’s team was 11 to 20.

We want to figure out which ratio is higher: 6/8 or 11/20 .

We can compare the ratios more easily if we express them as percentages.

First write the ratio 6/8 as a decimal. Then convert the decimal to a percentage.

6/8 = 0.75 = 75%

Do the same thing for 11/20

11/20 = 0.55 = 55%

Now compare the percentages.

75% ? 55%

75% is larger than 55%.

Emily’s team had a higher ratio of wins to losses.

✈️ Tiana and Aaron are solicitors. Tiana averages 12 civil cases and 10 criminal cases annually. Meanwhile, Aaron averages 17 civil cases and 13 criminal ones.

Which solicitor has a higher ratio of civil to criminal cases?

  • Tiana
  • Aaron
  • neither; the ratios are equivalent

For Tiana, the ratio of civil to criminal cases is 12 to 10. For Aaron, the ratio is 17 to 13.

We want to figure out which ratio is higher: 12/10 or 17/13 .

We can compare the ratios more easily if we express them as percentages.

First write the ratio 12/10 as a decimal. Then convert the decimal to a percentage.

12/10 = 1.2 = 120%

Do the same thing for 17/13 .

17 /13 ≈ 1.30769 = 130.769%

Now compare the percentages.

120% ? 130.769%

130.769% is larger than 120%.

Aaron has a higher ratio of civil to criminal cases.

let’s practice! 🖊️