Core Focus on Proportions & Probability

Lesson 1.5 Core Focus on Proportions & Probability Rate Conversions

Warm-Up Find each unit rate. 1. 2. Complete each conversion. 3. 4 yards = _____ feet 4. 80 centimeters = _____ meters 50 kilometers per hour 7.5 jobs per day 12 0.8

Lesson 1.5 Rate Conversions Convert rates to different units.

Vocabulary Rate Conversion A process of changing at least one unit of measurement in a rate to a different unit of measurement. Good to Know!  A conversion factor is a relationship between units of measure that is used to multiply or divide a ratio when converting from one system of units to another. Example: 1 yard = 3 feet  A conversion factor can be written as a rate in two ways: Example: 1 yard = 3 feet can be written  A conversion rate is equivalent to one, since the values in the numerator and denominator represent the same quantity.

Converting Rates • Write the original rate as a fraction. • Determine what unit needs to be changed. Write an appropriate conversion rate. • Multiply by the conversion rate. Cancel units. • Repeat steps 2 and 3 if changing more than one unit of measurement. • Simplify the final rate to a unit rate.

Example 1 Convert 48 miles per hour to miles per minute. Write the rate as a fraction. Choose one unit of measurement to convert 1 hour = 60 minutes first. Write the conversion factor that relates hours to minutes. Write the conversion factor as a conversion rate. Choose the conversion rate with “hours” in the numerator since “hours” is in the denominator of the original rate. or

Example 1 Continued… Convert 48 miles per hour to miles per minute. Multiply the original rate and the conversion rate. Cancel units. Simplify the rate to a unit rate. Forty-eight miles per hour is equal to 0.8 miles per minute.

Extra Example 1 Convert 54 miles per hour to miles per minute. 0.9 miles per minute

Example 2 Rolando rides his scooter 9 kilometers per hour. Find his rate in meters per minute. Write the rate as a fraction. Choose one unit of measurement to convert 1 hour = 60 minutes first. Write the conversion factor that relates hours to minutes. Write the conversion factor as a conversion rate. Choose the conversion rate with “hours” in the numerator since “hours” is in the denominator of the original rate. It does not matter which unit of measurement is changed first. or

Example 2 Continued… Rolando rides his scooter 9 kilometers per hour. Find his rate in meters per minute. Multiply the original rate and the conversion rate. Cancel rates. Write the conversion factor that relates 1 kilometer = 1,000 meters kilometers to meters. Write the conversion factor as a conversion with “kilometers” in the denominator since “kilometers” is in the numerator of the original rate.

Example 2 Continued… Rolando rides his scooter 9 kilometers per hour. Find his rate in meters per minute. Multiply the rate from the first conversion and the conversion rate. Cancel units. Simplify the rate to a unit rate. Rolando traveled 150 meters per minute on his scooter.

Extra Example 2 Pilar rides his skateboard 12 kilometers per hour. Find his rate in meters per minute. 200 meters per minute

Communication Prompt If you knew how fast your friend drove in feet per minute, how would you find the rate in miles per hour?

Exit Problems 1. Convert to . 2. Convert 30 feet per hour to feet per minute. 1,000 centimeters per minute 0.5 feet per minute

Core Focus on Proportions & Probability