8-1 Ratios and Rates Warm Up Problem of the Day Lesson Presentation Course 1 Warm Up Problem of the Day Lesson Presentation

8-1 Ratios and Rates Warm Up Write each fraction in simplest form. Course 1 8-1 Ratios and Rates 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 __

8-1 Ratios and Rates Problem of the Day Course 1 8-1 Ratios and Rates Problem of the Day What three consecutive odd numbers are factors of 105? 3, 5, 7

Course 1 8-1 Ratios and Rates Learn to write ratios and rates and to find unit rates.

Insert Lesson Title Here Course 1 8-1 Ratios and Rates Insert Lesson Title Here Vocabulary ratios equivalent ratios rate unit rate

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

8-1 Ratios and Rates 29 12 ___ 29 to 12 29:12 Course 1 8-1 Ratios and Rates 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.

8-1 Ratios and Rates Reading Math Course 1 8-1 Ratios and Rates Reading Math 29 12 ___ Read the ratio as “twenty-nine to twelve.”

Additional Example 1A: Writing Ratios Course 1 8-1 Ratios and Rates Additional Example 1A: Writing Ratios Use the table to write the ratio. A. cats to rabbits Animals at the Vet Cats 5 Dogs 7 Rabbits 2 or 5 to 2 or 5:2 5 2 __ Part to part

Additional Example 1B: Writing Ratios Course 1 8-1 Ratios and Rates Additional Example 1B: Writing Ratios Use the table to write the ratio. B. dogs to total number of pets Animals at the Vet Cats 5 Dogs 7 Rabbits 2 or 7 to 14 or 7:14 7 14 __ Part to whole

Additional Example 1C: Writing Ratios Course 1 8-1 Ratios and Rates Additional Example 1C: Writing Ratios Use the table to write the ratio. C. total number of pets to cats Animals at the Vet Cats 5 Dogs 7 Rabbits 2 or 14 to 5 or 14:5 14 5 __ Whole to part

8-1 Ratios and Rates Try This: Example 1A Course 1 8-1 Ratios and Rates Try This: Example 1A Use the table to write the ratio. A. birds to total number of pets Animals at the Vet Birds 6 Hamsters 9 Snakes 3 or 6 to 18 or 6:18 6 18 __ Part to whole

8-1 Ratios and Rates Try This: Example 1B Course 1 8-1 Ratios and Rates Try This: Example 1B Use the table to write the ratio. B. snakes to birds Animals at the Vet Birds 6 Hamsters 9 Snakes 3 or 3 to 6 or 3:6 3 6 __ Part to part

8-1 Ratios and Rates Try This: Example 1C Course 1 8-1 Ratios and Rates Try This: Example 1C Use the table to write the ratio. C. total number of pets to hamsters Animals at the Vet Birds 6 Hamsters 9 Snakes 3 or 18 to 9 or 18:9 18 9 __ Whole to part

Course 1 8-1 Ratios and Rates 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 Course 1 8-1 Ratios and Rates 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

8-1 Ratios and Rates Try This: Example 2 Course 1 8-1 Ratios and Rates Try This: 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

Course 1 8-1 Ratios and Rates 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 Course 1 8-1 Ratios and Rates Additional Example 3: Consumer Application A 3-roll pack of paper towels costs $2.79. A 6-roll 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-roll pack of paper towels is the better deal.

8-1 Ratios and Rates Try This: Example 3 Course 1 8-1 Ratios and Rates Try This: 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? $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.

Insert Lesson Title Here Course 1 8-1 Ratios and Rates Insert Lesson Title Here 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