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

Sunshine State Standards MA.6.A.2.2 Interpret and compare ratios and rates.

Vocabulary ratios equivalent ratios rate unit rate

For a time, a local symphony orchestra was made up of 95 musicians. Trombones Harp Percussion Trumpets Basses Violas 3 6 Horns 1 4 Clarinets 5 8 Double reeds Flutes 9 10 Cellos 12 29 Violins You can compare the different groups by using ratios. A ratio is a comparison of two quantities using division.

For example, you can use a ratio to compare the number of violins (29) with the number of violas (12). This ratio can be written in three ways. 29 12 ___ 29 to 12 29:12 Terms 29 12 ___ Notice that the ratio of violins to violas, is different from the ratio of violas to violins, . The order of the terms is important. 12 29 ___ Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part.

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 each ratio. 3 Snakes 9 Hamsters 6 Birds Animals at the Vet birds to total number of pets or 6 to 18 or 6:18 6 18 __ 1 _ Also or 1 to 3 or 1 : 3 3

Check It Out: Example 1B Use the table to write the ratio or rates. snakes to hamsters 3 Snakes 9 Hamsters 6 Birds Animals at the Vet or 3 to 9 or 3:9 3 9 __ 1 _ or 1 to 3 or 1 : 3 Also 3

Equivalent ratios are ratios that name the same comparison Equivalent ratios are ratios that name the same comparison. You can find an equivalent ratio by multiplying or dividing 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

Check It Out: Example 2 Write three equivalent ratios to compare the number of triangles to the number of hearts in the pattern. Possible answer : , and 3 9 __ 1 27

A rate compares two quantities that have different units of measure A rate compares two quantities that have different units of measure. Suppose a 2-liter bottle of soda costs $1.98. price number of liters _____________ $1.98 2 liters ________ rate = = $1.98 for 2 liters When the comparison is to one unit, the rate is called a unit rate. Divide both terms by the second term to find the unit rate. $1.98 2 _____ $1.98 ÷ 2 2 ÷ 2 ________ $0.99 1 _____ unit rate = = = $0.99 for 1 liter 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? $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 3A A 3-pack of juice boxes costs $2.10. A 9-pack costs $5.58. Which is the better deal? $2.10 3 _____ $5.58 9 ____ = $0.70 per box; = $0.62 per box The 9-pack is a better deal.

Check It Out: Example 3B A 24 oz bottle of apple juice costs $5.76. A 12 oz bottle of apple juice costs $3.84. Which is the better deal? $5.76 24 _____ $3.84 12 ____ = $0.24 per oz; = $0.32 per oz The 24 ounce bottle is a 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. Use 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