# Review of Unit 4 Vocabulary ratios equivalent ratios

Review of Unit 4

Vocabulary ratios equivalent ratios rate unit rate

For a time, the Boston Symphony Orchestra was made up of 95 musicians. Violins Cellos Flutes Double reeds 29 10 5 8 Violas Basses Trumpets Percussion 12 9 3 5 Clarinets Horns 4 6 Harp Trombones 1 3 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. Terms 29 ___ 12 29 to 12 29: 12 29 Notice that the ratio of violins to violas, ___ is 12 12. different from the ratio of violas to violins, ___ 29 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.

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

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

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

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

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

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

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

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

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

A rate compares two quantities that have different units of measure. Suppose a 2 -liter bottle of soda costs $1. 98. rate = price $1. 98 _______ = number of liters 2 liters $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 $0. 99 _____ $1. 98 _____ $0. 99 for 1 liter = = 2 2÷ 2 1 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 Write the rate. $5. 46 _____ 6 rolls Write the rate. $2. 79 ÷ 3 Divide both _____ 3 rolls ÷ 3 terms by 3. $5. 46 ÷ 6 Divide both _____ 6 rolls ÷ 6 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? $2. 10 _____ 3 pack Write the rate. $5. 58 _____ 9 pack Write the rate. $2. 10 ÷ 3 Divide both _____ 3 pack ÷ 3 terms by 3. $5. 58 ÷ 9 Divide both _____ 9 pack ÷ 9 terms by 9. $0. 70 _____ 1 box $0. 62 _____ 1 box $0. 70 for 1 juice box. $0. 62 for 1 juice box. The 9 -pack of juice boxes is the better deal.

Lesson Quiz Use the table to write ratio. each 1. tulips to daffodils 9: 17 2. crocuses to total number of bulbs 20: 51 3. total bulbs to lilies 51: 5 4. A dozen eggs cost $1. 25 at one market. At a 1 __ competing market, 1 dozen eggs cost $2. 00. 2 Which is the better buy? eggs from the first market

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