Slide 1: Warm Up Lesson Presentation Problem of the Day
Slide 2: 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
Slide 3: Problem of the Day
A carpenter can build one doghouse in one day. How many doghouses can 12 carpenters build in 20 days? 240
Slide 4: Learn to write and solve proportions.
Slide 5: Vocabulary proportion
Slide 6: 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
Slide 7: 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.
Slide 8: Additional Example 1 Continued
Now write the ratio of hearts to stars in each group. = A proportion shown by the model is = .
Slide 9: 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.
Slide 10: Check It Out: Example 1 Continued
Now write the ratio of faces to moons in each group. = A proportion shown by the model is = .
Slide 11: 8 • 2 = 4 • 4 5 • 9 = 3 • 15 16 = 16 45 = 45 6 • 3 = 9 • 2 18 = 18 7 • 2 = 14 • 1 14 = 14
Slide 12: 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
Slide 13: 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
Slide 14: 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.
Slide 15: In a proportion, the units must be in the same order in both ratios. Caution! = = or
Slide 16: 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.
Slide 17: 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.
Slide 18: 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.
Slide 19: 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 =