Lesson 1 Data Analysis Ratios and Rates

Warm-Up Simplify the following fractions. a. b. c. For each fraction below, write two equivalent fractions. a. b.

Ratios and Rates Targets: Understand the difference between ratios and rates. Apply ratios and rates to solve problems.

Vocabulary Ratios: Uses division to compare two numbers. Rates: A ratio comparing two numbers with different units. Unit Rates: A rate with a denominator of 1.

Writing a Ratio A ratio comparing two numbers, a and b, can be written in three ways: a : b a to b

Example 1a Use the table to find the following ratios. Write each ratio all three ways in simplest form. Ratio of girls to all students Total number of girls: 3 + 7 + 5 + 5 = 20 Total number of students: 5 + 6 + 8 + 3 + 20 = 42 Write ratios. 10:21 10 to 21

Example 1b Use the table to find the following ratios. Write each ratio all three ways in simplest form. Ratio of boys to girls Total number of boys: 5 + 6 + 8 + 3 = 22 Write ratios. 11:10 11 to 10

Example 2 A rectangular picture frame measures 4.5 feet long and 18 inches wide. What is the total ratio of the frame’s length to width? Convert units. 4.5(12) = 54 inches Ratio of length to width:

Example 3 Super cinemas sells a movie pass for $50 for admission into 8 movies. Movie Land sells a similar pass for $60 for admission into 10 movies. Which movie theater has the better deal? Super Cinemas: Movie Land: Movie Land is the better deal.

Exit Problems Identify each as either a ratio or a rate. 3 yards to 6 feet Convert $48 for 3 CD’s to a unit rate. A recipe calls for 2 cups of granulated sugar and 1 cup of brown sugar. What is the ratio of granulated sugar to total sugar?

Communication Prompt Describe the differences between a ratio, a rate and a unit rate. Give an example of each one.