Ratio, Proportion & Percent
For each of the following problems, consider how you would pose the same problem to your students. Would the wording need to change? Would you need to include more pictures? More detailed pictures? But remember we don't want to do TOO MUCH for the student. If we provide too much information, they will not need to think about what the question is asking.
Consider your problem-solving strategy for each of the following investigations. Is there another strategy that you could use? If so, which strategy would be more appropriate for understanding the concept?
A ratio compares two quantities that share a fixed, multiplicative relationship.
- A ratio is a fixed relationship. A fixed rate (e.g., $20.95 per person) and a fixed scale (e.g., one inch = 10 miles) both qualify as ratios. Relationships that are not fixed are not ratios (e.g., the relationship of the side of a square to the square's area is not fixed as you double the square's side. Thus, this relationship is not a ratio.).
- A ratio such as 3/5 indicates the size of each quantity compared (three and five) as well as represents a multiplicative (not an additive) relationship.
- A ratio compares two quantities in a particular order. The order is very important. For example, 24 miles per one gallon is very different from 24 gallons per one mile.
- The word "per" means "for every" and indicates a ratio. Examples of ratios include miles per gallon (gas mileage), dollars per hour (wages), cents per ounce (unit price), and people per square mile (population density).
It is important to note that ratios represent relative, rather than absolute, amounts. For example, if the ratio of boys to girls in a particular grade level is 2 to 3, there could be 20 boys and 30 girls, 200 boys and 300 girls, or some other pair of numbers whose ratio is equivalent (e.g., 40 boys and 60 girls).
Proportions are equivalent ratios. For example, 1 is to 3 as 2 is to 6 or 1/3 = 2/6 is a proportion.
Percents are simply another way of representing fractions, decimals, and ratios that are based on hundredths. For example, 12/100 or 0.12 can be thought of as 12%. "Percent" means "per hundred" or "for every 100." So, 12% is a way of representing 12 for every 100. Percents are an easy way to compare data because they have the common base of 100.