Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Write each fraction in simplest form. 1. 2. Warm Up Write each fraction in simplest form. 1. 2. 3. 4. 2 6 __ 1 3 __ 4 16 __ 1 4 __ 25 70 ___ 5 14 __ 6 52 __ 3 26 __

What three consecutive odd numbers are factors of 105? Problem of the Day What three consecutive odd numbers are factors of 105? 3, 5, 7

Learn to write ratios and rates and to find unit rates.

Vocabulary ratios equivalent ratios rate unit rate

Choose your fast food restaurant Chick-Fil-A: Sonic: Subway: You can compare the different groups by using ratios. ratio is a comparison of two quantities using division. Ex: comparing fast food restaurants

Ratios can be written to compare: For example, you can use a ratio to compare the number of people who like one fast food place over another. A ratio can be written in three ways. to : . The order of the terms is important. Ratios can be written to compare:

Read the ratio as “twenty-nine to twelve.” Reading Math 29 12 ___ Read the ratio as “twenty-nine to twelve.”

Additional Example 1A: Writing Ratios Use the table to write the ratio. cats to rabbits 2 Rabbits 7 Dogs 5 Cats Animals at the Vet or 5 to 2 or 5:2 5 2 __ Part to part

Additional Example 1B: Writing Ratios Use the table to write the ratio. dogs to total number of pets 2 Rabbits 7 Dogs 5 Cats Animals at the Vet or 7 to 14 or 7:14 7 14 __ Part to whole

Additional Example 1C: Writing Ratios Use the table to write the ratio. total number of pets to cats 2 Rabbits 7 Dogs 5 Cats Animals at the Vet or 14 to 5 or 14:5 14 5 __ Whole to part

Check It Out: Example 1A Use the table to write the ratio. birds to total number of pets 3 Snakes 9 Hamsters 6 Birds Animals at the Vet or 6 to 18 or 6:18 6 18 __ Part to whole

Check It Out: Example 1B Use the table to write the ratio. snakes to birds 3 Snakes 9 Hamsters 6 Birds Animals at the Vet or 3 to 6 or 3:6 3 6 __ Part to part

Check It Out: Example 1C Use the table to write the ratio. total number of pets to hamsters 3 Snakes 9 Hamsters 6 Birds Animals at the Vet or 18 to 9 or 18:9 18 9 __ Whole to part

Equivalent ratios are ratios that name the same comparison. They are = To Find: Multiply or Divide both terms of a ratio by the same number.

Additional Example 2: Writing Equivalent Ratios Write three equivalent ratios to compare the number of diamonds to the number of spades in the pattern. number of diamonds 3 6 __ There are 3 diamonds and 6 spades. = number of spades 3 6 __ 3 ÷ 3 6 ÷ 3 ____ 1 2 __ There is 1 diamond for every 2 spades. = = 3 6 __ 3 • 3 6 • 3 9 18 __ If you triple the pattern, there will be 9 diamonds for 18 spades. = = So , , and are equivalent ratios. 3 6 __ 1 2 9 18

There are 3 triangles and 9 hearts. number of hearts Check It Out: Example 2 Write three equivalent ratios to compare the number of triangles to the number of hearts in the pattern. number of triangles 3 9 __ There are 3 triangles and 9 hearts. = number of hearts 3 9 __ 3 ÷ 3 9 ÷ 3 ____ 1 3 __ There is 1 triangle for every 3 hearts. = = If you triple the pattern, there will be 9 triangles for 27 hearts. 3 9 __ 3 • 3 9 • 3 9 27 __ = = So , , and are equivalent ratios. 3 9 __ 1 27

A rate compares two quantities that have different units of measure. EX: a 2 liter bottle costs $1.98 2 lbs. of hamburger costs $11.98 unit rate. * want the price of 1 unit (ITEM) Divide both terms to find the unit rate. unit rate = $1.98 2 _____ $0.99 1 _____ = $0.99 for 1 liter

16 miles in 4 hours = 3 oranges for $2.40= 3 bottles for .93= 6 DVD’s for $36.60 = When the prices of two or more items are compared, the item with the lowest unit rate is the best deal.

Additional Example 3: Consumer Application A 3-pack of paper towels costs $2.79. A 6-pack of the same paper towels costs $5.46. Which is the better deal? WHY? $2.79 3 rolls _____ $5.46 6 rolls _____ Write the rate. Write the rate. $2.79 ÷ 3 3 rolls ÷ 3 _________ Divide both terms by 3. $5.46 ÷ 6 6 rolls ÷ 6 _________ Divide both terms by 6. $0.93 1 roll _____ $0.91 1 roll _____ $0.93 for 1 roll. $0.91 for 1 roll. The 6-pack of paper towels is the better deal.

Check It Out: Example 3 A 3-pack of juice boxes costs $2.10. A 9-pack of the same juice boxes costs $5.58. Which is the better deal? WHY? $2.10 3 pack _____ $5.58 9 pack _____ Write the rate. Write the rate. $2.10 ÷ 3 3 pack ÷ 3 _________ Divide both terms by 3. $5.58 ÷ 9 9 pack ÷ 9 _________ Divide both terms by 9. $0.70 1 box _____ $0.62 1 box _____ $0.62 for 1 juice box. $0.70 for 1 juice box. The 9-pack of juice boxes is the better deal.

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Use the table to write each ratio. 1. tulips to daffodils Lesson Quiz Use the table to write each ratio. 1. tulips to daffodils 2. crocuses to total number of bulbs 3. total bulbs to lilies 4. A dozen eggs cost $1.25 at one market. At a competing market, 1 dozen eggs cost $2.00. Which is the better buy? 9:17 20:51 51:5 1 2 __ eggs from the first market

Lesson Quiz for Student Response Systems 1. Use the table to identify the ratio of lions to elephants. A. 8:7 B. 8:12 C. 7:8 D. 7:12 Animals in a Zoo Lions 8 Tigers 12 Elephants 7 Others 15

Lesson Quiz for Student Response Systems 2. Use the table to identify the ratio of game CDs to total number of CDs. A. 25:8 B. 17:8 C. 8:17 D. 8:25 Gina’s CD Collection Music 5 Games 8 Cartoons 12

Lesson Quiz for Student Response Systems 3. Using the table to identify the ratio of total number of grades to number of students with a C. A. 9:30 B. 9:21 C. 21:9 D. 30:9 Grades on Final Exam A 8 B 13 C 9

Lesson Quiz for Student Response Systems 4. Jeff sells a pack of 36 pencils for $3.25. Betsy sells a pack of 12 pencils for $1.50. Which is the better buy? A. a pack of 12 pencils from Betsy B. a pack of 36 pencils from Jeff C. Both D. None