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Lesson Menu Objectives Vocabulary Example 1 Example 2 Example 3 Example 4 Quick Quiz

Objectives To set up and solve proportions To use proportions and similar triangles to calculate distances To recognize proportions as pairs of equivalent ratios

Vocabulary proportion map scale angle of elevation proportional relationship

Example 1 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 1Find a pattern and extend it. For 2 cups of beans, you would need a total of or 10 cups of water.

Example 1 Continue this pattern until you reach 4 cups. Method 2Multiply each quantity by the same number. Since 1 × 4 = 4, multiply each quantity by 4.

Example 1 Answer: So, you would need 20 cups of water for 4 cups of beans.

Example 1 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 cups 1.A 2.B 3.C 4.D

Example ● n=14 ● 6Find the cross products. 3.5n=84Multiply. Write the proportion. Divide each side by 3.5. n=24Simplify. Solving Proportions

Example 2 Answer: The solution is 24.

1.A 2.B 3.C 4.D Example 2 A.w = 5.25 B.w = 5.5 C.w = 5.75 D.w = 6.25

Example 3 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

Example 3 Answer: The tree is 22 feet tall. tree’s shadowtree’s height Marcel’s shadowMarcel’s height 12 ● 5.5 = 3 ● hFind the cross products. Multiply. Simplify. Divide each side by 3.

1.A 2.B 3.C 4.D Example 3 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

Example 4 Graph each rational number on a number line. Mark off equal size increment of between –4 and –3. Answer: The number line shows that.

Example 4 A.> B.< C.= 1.A 2.B 3.C

1.A 2.B 3.C 4.D Quick Quiz 1 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.D Quick Quiz 2 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.D Quick Quiz 3 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.D Quick Quiz 4 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 feet D.22 feet

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Resources Image Bank Math Tools Multilingual e-Glossary Using a Percent Model Solving Proportions Similar Triangles

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