Lesson 1 3 Core Focus on Ratios Rates

Lesson 1. 3 Core Focus on Ratios, Rates and Statistics Customary Conversions

Warm-Up Write the first four terms of a geometric sequence with the given first term and ratio. 1. first term: 1 ratio: 3 1, 3, 9, 27, … 2. first term: 10, 000 ratio: 10, 000, 100, 10 3. Determine whether or not the sequence is a geometric sequence. Explain why or why not. 5, 10, 15, 20, 25, … Not a geometric sequence. The terms have a difference of 5 but not a ratio between them of 5. Complete each blank. 4. 1 foot = ____ 12 inches 5. 1 hour = ____ 60 minutes

Lesson 1. 3 Customary Conversions Convert customary measurements.

Vocabulary Conversion The process of renaming a measurement using different units. Good to Know! Customary units are units of measure that include inches, feet, yards and miles for measuring length, ounces, tons and pounds for weight and cups, pints, quarts and gallons for volume. The customary system of measurement is used in the United States. Sometimes it is necessary to convert from one unit to another. Smaller units can be converted to larger units, like inches to feet. Larger units can be converted to smaller units, like days to hours.

Example 1 Choose a reasonable estimate. Explain your reasoning for each choice. a. amount of water in a personal water bottle: 1 quart or 1 gallon 1 quart. Think about a gallon of milk. That is larger than a personal water bottle. b. length of a couch: 6 yards or 6 feet. People are measured in feet. A 6 foot person could lay on a couch. Think about yards on a football field. Six yards would make a very long couch. c. weight of an elephant: 2 pounds or 2 tons. Elephants are quite large. Most human babies weigh more than 2 pounds when they are born.

Example 2 Using the information in the conversion table, find the number of yards in 36 feet. Feet 3 6 9 12 24 36 Yards 1 2 3 4 8 ? Each pair of feet and yard values shows the ratio of feet to yards. Choose any ratio and write it as a fraction. Simplify the ratio, if needed. Find an equivalent ratio with 36 feet. There are 12 yards in 36 feet.

Unit Conversions When converting to smaller units, MULTIPLY ( ). When converting to larger units, DIVIDE ( ).

Example 3 Complete the conversion. a. 2 miles = _______ feet Find the conversion factor. 1 mile = 5, 280 feet Multiply 2 miles by 5, 280. 2 5280 = 10560 2 miles = 10, 560 feet. When converting to a smaller unit, multiply.

Example 3 Continued… Complete the conversion. b. 280 days = _______ weeks Find the conversion factor. 1 week = 7 days Divide 280 by 7. 280 7 = 40 280 days = 40 weeks. When converting to a larger unit, divide.

Example 3 Continued… Complete the conversion. c. 18 inches = _______ feet Find the conversion factor. 1 foot = 12 inches Divide 18 by 12. 18 12 = 1. 5 18 inches = 1. 5 feet.

Communication Prompt Explain a situation where you would want to change units from inches to feet or feet to yards. How would you change the units?

Exit Problems Complete each conversion. 1. 3 weeks = _____ 21 days 2. 90 minutes = _____ 1. 5 hours 3. 4 yards = _____ 12 feet