Transcript Slide 1
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Proportions
Lesson Presentation Lesson Quizzes
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Proportions
Warm Up Use the table to write each ratio.
Brown bears Giraffes Monkeys Polar Bears 3 2 17 4
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.
2 1 = 4 2
Reading Math
4 2 = 8 4 2 1 = 6 3 one as four is to two.”
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Additional Example 1: Modeling Proportions Write a proportion for the model.
First write the ratio of hearts to stars.
number of hearts number of stars = 4 8 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.
number of hearts number of stars = 2 4
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Check It Out: Example 1 Write a proportion for the model.
First write the ratio of faces to moons.
number of faces number of moons = 2 6 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.
number of faces number of moons = 1 3
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CROSS PRODUCTS Cross products in proportions are equal
8 • 4 8 = 2 = 2 4 4 • 4 16 = 16 5 • 3 5 = 9 = 9 15 3 • 15 45 = 45 9 6 6 • 3 = = 3 2 9 • 2 18 = 18 14 7 7 • 2 = = 2 1 14 • 1 14 = 14
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Additional Example 2: Using Cross Products to Complete Proportions Find the missing value in the proportion.
5 6 =
n
18 6 •
n
= 5 • 18
Find the cross products.
The cross products are equal.
6n 6n 6 = 90 = 90 6
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.
3 5 =
n
15 5 •
n
= 3 • 15 5n = 45 5n 5 = 45 5 n = 9
Find the cross products.
The cross products are equal.
n is multiplied by 5.
Divide both sides by 5 to undo the multiplication.
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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?
1 tbsp 6 gal 1 tbsp 6 gal
f
4 gal
f
4 gal 6 •
f
= 1 • 4
Let f be the amount of fertilizer for 4 gallons of water.
Write a proportion.
The cross products are equal.
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Caution!
In a proportion, the units must be in the same order in both ratios.
or
tbsp gal gal tbsp
= =
tbsp gal gal tbsp
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Additional Example 3 Continued
6f = 4 6f 6 = 4 6
f is multiplied by 6.
Divide both sides by 6 to undo the multiplication.
Write your answer in simplest form.
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?
3 tbsp 9 gal 3 tbsp 9 gal
f
2 gal
f
2 gal 9 •
f
= 3 • 2
Let f be the amount of fertilizer for 2 gallons of water.
Write a proportion.
The cross products are equal.
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Check It Out: Example 3 Continued
9f = 6 9f 9 = 6 9
f is multiplied by 9.
Divide both side by 9 to undo the multiplication.
Write your answer in simplest form.
You would use tbsp of fertilizer for 2 gallons of water.
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Lesson Quizzes
Lesson Quiz for Student Response Systems
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Lesson Quiz
1. Write a proportion for the model.
2 6 = 1 3
Find the missing value in each proportion.
2.
9 5 = __ x
3.
p
36 = 5 6 x = 25 p = 30 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?
9 g
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Lesson Quiz for Student Response Systems 1. Identify a proportion for the model. A. C. B. D.
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Lesson Quiz for Student Response Systems 2. Identify the missing value in the proportion.
A. x = 168 B. x = 56 C. x = 72 D. x = 49
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Lesson Quiz for Student Response Systems 3. Identify the missing value in the proportion.
A. n = 6 B. n = 51 C. n = 34 D. n = 102
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Lesson Quiz for Student Response Systems 4. According to the label, 1 tablespoon of mixed fruit concentrate should be used to prepare 200 ml of juice. How many tablespoons of concentrate would you use to prepare 800 ml of juice?
A. 2 tbsp B. 3 tbsp C. 4 tbsp D. 5 tbsp