1. PRE-ALGEBRA

2. Lesson 6-1 Warm-Up

3. PRE-ALGEBRA What is a “ratio”? How do you write a ratio? ratio: a comparison of two numbers by division – There are three ways to compare two numbers: a to b a : b You can write a ratio to compare a part to a part or part to a whole. The first item being compared is always the first number and the second item being compared is the second number of the ratio. Example: A recipe calls for 4 cups of cereal and 2 cups of pretzels. Write this as a ratio. a ba b read as “to” Ratios and Unit Rates (6-1)

4. PRE-ALGEBRA What is a “rate”? What is a “unit rate”? rate: a ratio that compares two quantities measured in different units. Example: is read as “120 miles ‘per’ or ‘each’ 4 hours” unit rate: the rate in which the denominator is 1 (rate ‘per’ 1 unit of a given quantity) - Unit rate is used in everyday life to determine the best value. It can be found by simplifying the fraction to a denominator of “1” or simply dividing the numerator (top number) by the denominator (bottom number. Example: = or 120  4 = 30 mph The above unit rate is read as “30 miles ‘per’ hour” (30 m/h or 30 mph) 120 miles 4 hours 120 miles 4 hours  4 30 miles 1 hours Ratios and Unit Rates (6-1)

5. PRE-ALGEBRA Find the unit rate for typing 145 words in 5 minutes. = 29 words/minute Divide. number of words number of minutes 145 words 5 minutes = Write a rate comparing words to minutes. The unit rate is 29 words per minute. LESSON 6-1 Additional Examples Ratios and Unit Rates

6. PRE-ALGEBRA Convert 30 gal/min to cups/second. 30 gal/min = 30 gal 1 min 16 c 1 gal 1 min 60 s Convert gallons to cups and minutes to seconds. 1 min 1 2 60 s Divide the common factors and units. = 1 30 gal 1 min 8 16 c 1 gal = 8 c s Simplify. 30 gal/min equals 8 c/s. Ratios and Unit Rates LESSON 6-1 Additional Examples

7. PRE-ALGEBRA The table shows prices for different packages of index cards. Which size has the lowest unit cost? Price $2.70 $1.30 $.75 100 50 25 Size (cards) 100 cards: price number of cards $2.70 100 cards = $.027/card25 cards: price number of cards $.75 25 cards = $.03/card The 50-card pack has the lowest unit cost. 50 cards: price number of cards $1.30 50 cards = $.026/card Find the unit costs. Ratios and Unit Rates LESSON 6-1 Additional Examples

8. PRE-ALGEBRA Painting several rooms will take 36 person-hours. How long will it take for 4 painters? It takes 36 persons to complete painting several rooms in 1 hour. To find the number of hours it will take 4 persons to complete the job, divide. 36 person-hours 4 persons = 9 hours Divide the number of person-hours by the number of workers. It will take 9 hours for 4 painters to paint the rooms. Check Since = hours, the units check. person hours persons Ratios and Unit Rates LESSON 6-1 Additional Examples

9. PRE-ALGEBRA Find each unit rate. 1.You pay $4.50 for 2 gallons of orange juice. 2.You pay $21.60 for a 20-lb bag of dog food. 3. A bird flies at a speed of 384 in./s. What is its speed in units of ft/min? 4. A job takes 96 person-days. How many workers are needed to complete the job in 24 days? $2.25/gal $1.08/lb 1,920 ft/min 4 Lesson Quiz Ratios and Unit Rates LESSON 6-1