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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 1 12. 1 15. Warm Up Write each fraction in simplest form. 4 48. 9 135. 2. 1. Convert the following measurements. 3. 192 inches = feet. 16. 4. 18.5 feet = inches. 222. 5. 324 inches = feet. 27.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 1 12 1 15 Warm Up Write each fraction in simplest form. 4 48 9 135 2. 1. Convert the following measurements. 3. 192 inches = feet 16 4. 18.5 feet = inches 222 5. 324 inches = feet 27

  3. California Standards NS1.3 Use proportions to solve problems (e.g., determine the value of N if T = , find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. 4 7 N 21

  4. Vocabulary scale model scale factor scale scale drawing

  5. This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO gauge model train is . 1 87 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train.

  6. A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train. A scale drawingis a proportional two-dimensional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

  7. 13.5 108 18 144 1 8 The scale factor is . Additional Example 1: Finding a Scale Factor Identify the scale factor. You can use the lengths or widths to find the scale factor. 1 8 blueprint length room length = = Write a ratio. Then simplify. 1 8 blueprint width room width = = Write a ratio. Then simplify.

  8. 1 6 The scale factor is . Check It Out! Example 1 Identify the scale factor. blueprint length aircraft length 2 12 1 6 = Write a ratio. Then simplify. = blueprint wing span aircraft wing span 3 18 1 6 = Write a ratio. Then simplify. =

  9. Additional Example 2: Using Scale Factors to Find Unknown Lengths A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the original photograph to the nearest tenth of an inch. 5 1 poster photo 5 1 = Think: 36 l 5 1 Write a proportion to find the length l. = 5l = 36 Find the cross products. l= 7.2 Divide.

  10. Additional Example 2 Continued A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches. The scale factor is . Find the size of the photograph. 5 1 poster photo 5 1 = Think: 20.5 w 5 1 Write a proportion to find the width w. = 5w = 20.5 Find the cross products. w= 4.1 Divide. The photo is 7.2 in. long and 4.1 in. wide.

  11. l 45 1.5 1 = Check It Out! Example 2 Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 = Think: Write a proportion to find the length l. Find the cross products. l = 45 · 1.5 l= 67.5 Multiply.

  12. Check It Out! 2 Continued Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale factor is . Find the size of the dollhouse. 1.5 1 dollhouse blueprint 1.5 1 = Think: Write a proportion to find the width w. w 24 1.5 1 = w = 24 · 1.5 Find the cross products. w= 36 Multiply. The dollhouse is 67.5 inches long and 36 inches wide.

  13. Additional Example 3: Measurement Application On a road map with a scale of 1.5 inches = 60 miles, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities? Let d be the actual distance between the cities. 1.5 60 7.5 d = Write a proportion. 1.5 · d = 60 · 7.5 Find the cross product. 1.5d = 450 Multiply. 450 1.5 1.5d 1.5 = Divide both sides by 1.5. d = 300 The distance between the cities is 300 miles.

  14. Check It Out! Example 3 On a road map with a scale of 1 inch = 50 kilometers, the distance between Dallas and Houston is 7 inches. What is the actual distance between the two cities? Let d be the actual distance between the cities. 1 50 7 d = Write a proportion. Find the cross products. 1 · d = 50 · 7 1d = 350 Multiply. d = 350 The distance between the cities is 350 kilometers.

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