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Objectives
Vocabulary
Example 1
Example 2
Example 3
Example 4
Quick Quiz
• To set up and solve proportions
• To use proportions and similar triangles to calculate distances
• To recognize proportions as pairs of equivalent ratios
• proportion
• map scale
• angle of elevation
• proportional relationship
BEANS A recipe calls for 5 cups of water for each cup of pinto beans. Use the ratio table to find how many cups of water should be used for 4 cups of pinto beans.
Method 1 Find a pattern and extend it.
For 2 cups of beans, you would need a total of 5 + 5 or 10 cups of water.
Continue this pattern until you reach 4 cups.
Method 2 Multiply each quantity by the samenumber.
Since 1 × 4 = 4, multiply each quantity by 4.
Answer: So, you would need 20 cups of water for 4 cups of beans.
PUNCH A recipe for punch calls for 3 cups of juice for every cup of soda. Use the ratio table to find how many cups of juice should be used for 5 cups of soda.
A. 11 cups
B. 13 cups
C. 15 cups
D. 17 cups0% 0%0%0%
1. A
2. B
3. C
4. D
3.5 ● n = 14 ● 6Find the cross
products.
3.5n = 84Multiply.
Write the proportion.
Divide each side by 3.5.
n = 24Simplify.
Solving Proportions
1. A
2. B
3. C
4. D
0% 0%0%0%
A. w = 5.25
B. w = 5.5
C. w = 5.75
D. w = 6.25
TREES A tree in front of Marcel’s house has a shadow 12 feet long. Marcel’s shadow is 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree?
Similar Triangles
Answer: The tree is 22 feet tall.
tree’s shadow tree’s heightMarcel’s shadow Marcel’s height
12 ● 5.5 = 3 ● h Find the cross products.
Multiply.
Simplify.
Divide each side by 3.
1. A
2. B
3. C
4. D0% 0%0%0%
Jayson casts a shadow that is 10 feet long. At the same time, a flagpole casts a shadow that is 40 feet long. If the flagpole is 20 feet tall, how tall is Jayson?
A. 4.5 feet
B. 5 feet
C. 5.5 feet
D. 6 feet
Graph each rational number on a number line. Mark off
equal size increment of between –4 and –3.
Answer: The number line shows that .
1. A
2. B
3. C
4. D0% 0%0%0%
Mixture A is made up of 6 containers of paint, 4 yellow and 2 blue. Mixture B is made up of 9 containers of paint, 5 yellow and 4 blue. How many yellow containers of paint should be added to Mixture B so that it is proportional to Mixture A?
A. 2 containers
B. 3 containers
C. 4 containers
D. 6 containers
1. A
2. B
3. C
4. D0% 0%0%0%
Hobson School has a student-teacher ratio of 9:2 for their current school year. Next year the enrollment of the school is expected to be 178 students. How many teachers will be employed next year?
A. 20 teachers
B. 39 teachers
C. 10 teachers
D. 40 teachers
1. A
2. B
3. C
4. D0% 0%0%0%
A map has a scale of 3 centimeters equals 100 miles. If two cities are 12.5 centimeters apart, approximately how many miles separate the cities?
A. about 417 miles
B. about 37.5 miles
C. about 24 miles
D. about 400 miles
1. A
2. B
3. C
4. D0% 0%0%0%
A 25 foot tall flag pole casts an 8 foot shadow on the ground. A nearby tree casts a 14 foot shadow. How tall is the tree?
A. 17 feet
B. 32 feet
C. 43.75 feet
D. 22 feet
Image Bank
Math Tools
Multilingual e-Glossary
Using a Percent Model
Solving Proportions
Similar Triangles
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