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

Learn how to write ratios, find unit rates & compare quantities using real-life examples. Practice equivalent ratios in a symphony orchestra context.

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

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

  2. Vocabulary ratios equivalent ratios rate unit rate

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

  4. 29 ___ 12 29 ___ 12 12 ___ 29 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 to 12 29:12 Terms Notice that the ratio of violins to violas, is different from the ratio of violas to violins, . The order of the terms is important. Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part.

  5. 29 ___ 12 Reading Math Read the ratio as “twenty-nine to twelve.”

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

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

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

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

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

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

  12. 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.

  13. 3 __ 6 3 3 ÷ 3 1 __ __ ____ 6 6 ÷ 3 2 3 3 • 3 9 __ __ 6 6 • 3 18 3 1 9 __ __ __ So , , and are equivalent ratios. 6 2 18 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 There are 3 diamonds and 6 spades. = number of spades There is 1 diamond for every 2 spades. = = If you triple the pattern, there will be 9 diamonds for 18 spades. = =

  14. 3 __ 9 3 3 ÷ 3 1 __ __ ____ 9 9 ÷ 3 3 3 3 • 3 9 __ __ 9 • 3 9 27 3 1 9 __ __ __ So , , and are equivalent ratios. 9 3 27 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 There are 3 triangles and 9 hearts. = number of hearts There is 1 triangle for every 3 hearts. = = If you triple the pattern, there will be 9 triangles for 27 hearts. = =

  15. price $1.98 _____________ ________ number of liters 2 liters $1.98 $1.98 ÷ 2 $0.99 _____ ________ _____ 2 2 ÷ 2 1 Aratecompares two quantities that have different units of measure. Suppose a 2-liter bottle of soda costs $1.98. $1.98 for 2 liters rate = = 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. $0.99 for 1 liter unit rate = = = When the prices of two or more items are compared, the item with the lowest unit rate is the best deal.

  16. $2.79 $5.46 _____ _____ 3 rolls 6 rolls $2.79 ÷ 3 $5.46 ÷ 6 _________ _________ 3 rolls ÷ 3 6 rolls ÷ 6 $0.93 $0.91 _____ _____ 1 roll 1 roll 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? Write the rate. Write the rate. Divide both terms by 3. Divide both terms by 6. $0.91 for 1 roll. $0.93 for 1 roll. The 6-pack of paper towels is the better deal.

  17. $2.10 $5.58 _____ _____ 3 pack 9 pack $2.10 ÷ 3 $5.58 ÷ 9 _________ _________ 3 pack ÷ 3 9 pack ÷ 9 $0.70 $0.62 _____ _____ 1 box 1 box 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? Write the rate. Write the rate. Divide both terms by 3. Divide both terms by 9. $0.62 for 1 juice box. $0.70 for 1 juice box. The 9-pack of juice boxes is the better deal.

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