Ratio and Proportion

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Warm Up Lesson Presentation Problem of the Day

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Warm Up Use the table to write each ratio. 1. giraffes to monkeys 2. polar bears to all bears 3. monkeys to all animals 4. all animals to all bears 2:17 4:7 17:26 26:7

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Problem of the Day A carpenter can build one doghouse in one day. How many doghouses can 12 carpenters build in 20 days? 240

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Learn to write and solve proportions.

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Vocabulary proportion

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A proportion is an equation that shows two equivalent ratios. Read the proportion = as “two is to one as four is to two.” Reading Math

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Additional Example 1: Modeling Proportions Write a proportion for the model. = First write the ratio of hearts to stars. Next separate the hearts and stars into two equal groups.

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Additional Example 1 Continued Now write the ratio of hearts to stars in each group. = A proportion shown by the model is = .

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Check It Out: Example 1 Write a proportion for the model. = First write the ratio of faces to moons. Next separate the faces and moons into two equal groups.

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Check It Out: Example 1 Continued Now write the ratio of faces to moons in each group. = A proportion shown by the model is = .

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8 • 2 = 4 • 4 5 • 9 = 3 • 15 16 = 16 45 = 45 6 • 3 = 9 • 2 18 = 18 7 • 2 = 14 • 1 14 = 14

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Additional Example 2: Using Cross Products to Complete Proportions Find the missing value in the proportion. Find the cross products. 6 • n = 5 • 18 The cross products are equal. 6n = 90 n is multiplied by 6. = Divide both sides by 6 to undo the multiplication. n = 15

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Check It Out: Example 2 Find the missing value in the proportion. Find the cross products. 5 • n = 3 • 15 The cross products are equal. 5n = 45 n is multiplied by 5. = Divide both sides by 5 to undo the multiplication. n = 9

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Additional Example 3: Measurement Application According to the label, 1 tablespoon of plant fertilizer should be used per 6 gallons of water. How many tablespoons of fertilizer would you use for 4 gallons of water? = Let f be the amount of fertilizer for 4 gallons of water. = Write a proportion. 6 • f = 1 • 4 The cross products are equal.

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In a proportion, the units must be in the same order in both ratios. Caution! = = or

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Additional Example 3 Continued f is multiplied by 6. Divide both sides by 6 to undo the multiplication. Write your answer in simplest form. 6f = 4 = f = tbsp You would use tbsp of fertilizer for 4 gallons of water.

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Check It Out: Example 3 According to the label, 3 tablespoons of plant fertilizer should be used per 9 gallons of water. How many tablespoons of fertilizer would you use for 2 gallons of water? = Let f be the amount of fertilizer for 2 gallons of water. = Write a proportion. 9 • f = 3 • 2 The cross products are equal.

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Check It Out: Example 3 Continued f is multiplied by 9. Divide both side by 9 to undo the multiplication. Write your answer in simplest form. 9f = 6 = f = tbsp You would use tbsp of fertilizer for 2 gallons of water.

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Lesson Quiz 1. Write a proportion for the model. Find the missing value in each proportion. 2. = 3. = 4. The label on a bottle of salad dressing states that there are 3 grams of fat per tablespoon. If you use 3 tablespoons, how many grams of fat would you be getting? p = 30 x = 25 9 g =