RRPR - Ratios, Rates, and Unit Rates Lesson
Ratios, Rates, and Unit Rates
A ratio is a comparison of two numbers. Ratios are used often in everyday life to compare amounts of different things. In sports, you might hear someone talk about the win to loss record of a team, or the baseball pitcher's win to loss record, or a quarterback's ratio of completed passes to total attempts. In architecture and art, the golden ratio is the "perfect" relationship of the length and width of a rectangle. In cooking a cake, there is a certain ratio of the amount of sugar to the amount of flour that is used.
There are several ways to write a ratio. In a classroom, if there are 2 boys and 4 girls, the ratio of boys to girls can be written as 2 to 4, 2:4, or 2/4. You would read all of these as "two to four." Notice that in the expression "boys to girls", "boys" is first in our example. It is very important to know which one comes first. The number of the first one must be written first, or in the numerator, of the ratio. If the problem was written as "girls to boys", the ratio would use the number of girls first, like 4:2 or 4/2.
To compare two ratios, write them as fractions and reduce the fractions to the lowest terms. If the fractions are the same, the ratios are equal. If one ratio is 6/8 and the other is 12/16, you would need to reduce both fractions, using the Greatest Common Factor (GCF) of 4, to see that they are both equal to 3/4. To reduce a fraction to the lowest terms, the numerator and denominator must be divided by the Greatest Common Factor.
A rate is a ratio. A ratio is a comparison of two numbers. A ratio can be expressed three ways:
- Using the fraction bar as in 2/3.
- Using a colon symbol as in 2:3 .
- Using the word "to" as in 2 to 3.
Unit Rate
When the denominator of a rate is 1, we call that rate a unit rate. We usually use the keyword "per" or the division symbol to indicate a unit rate. For example: If a student earns $7.65 per hour, it is the same as $7.65 per hour or $7.65/hour. This means $7.65 for every hour of work. Unit rates can also be used to solve problems.
Watch the video below to learn how to use rates to solve problems.
Other examples of rate include speed, which is distance per time, and mileage, which is distance per quantity of fuel used.
Watch the following video as an example of finding a rate.
Use the activity below to learn more about units of measure.
Ratio Tables
As you have seen in the video, reducing fractions and equivalent fractions are ways to find ratios. A ratio table is another way of finding answers to ratio problems. With a ratio table, you start with a known ratio and use it to find other numbers with the same ratio. You can keep using the numbers you find to discover more numbers until you solve the problem.
For example, Ms. Lampert organizes a summer camp for children. This year, 169 children have signed up for camp. Ms. Lampert needs to figure out how many tents will accommodate 169 children. Each tent is large enough for 12 children. Here is how you can solve this problem using a ratio table.
In the first column, you have 1 tent that can hold 12 children. The second column is where we multiply both numbers of the 1st column by ten. The third column is where we divide both numbers in the previous column by 2. The fourth column is where we multiply both numbers in the previous column by 3. The fifth column is where we subtract the numbers in the first column from those in the fourth column.
QUESTION: To answer Ms. Lampert's question using the ratio table, you found that 14 tents can hold 168 children. However, there are 169 children, so one extra tent is needed.
ANSWER: Ms. Lampert needs 15 tents.
Rate and Ratio Homework #1 Assignment
IMAGES CREATED BY GAVS