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Holt CA Course 1 5-8Scale Drawings and Scale Models Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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Holt CA Course 1 5-8Scale Drawings and Scale Models Warm Up Write each fraction in simplest form Convert the following measurements inches = feet feet = inches inches = feet

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Holt CA Course 1 5-8Scale Drawings and Scale Models 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. California Standards 4747 N 21

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Holt CA Course 1 5-8Scale Drawings and Scale Models Vocabulary scale model scale factor scale scale drawing

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Holt CA Course 1 5-8Scale Drawings and Scale Models 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 This means that each dimension of the model is of the corresponding dimension of the actual train. 1 87

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Holt CA Course 1 5-8Scale Drawings and Scale Models 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 drawing is a proportional two- dimensional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

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Holt CA Course 1 5-8Scale Drawings and Scale Models Identify the scale factor. Additional Example 1: Finding a Scale Factor RoomBlueprint Length (in.)14418 Width (in.) blueprint length room length = The scale factor is. Write a ratio. Then simplify = You can use the lengths or widths to find the scale factor. blueprint width room width = 1818 Write a ratio. Then simplify =

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Holt CA Course 1 5-8Scale Drawings and Scale Models Check It Out! Example 1 Identify the scale factor. Model AircraftBlueprint Length (in.)122 Wing span (in.)183 blueprint length aircraft length = 2 12 = 1616 Write a ratio. Then simplify. The scale factor is blueprint wing span aircraft wing span = 3 18 = 1616 Write a ratio. Then simplify.

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Holt CA Course 1 5-8Scale Drawings and Scale Models 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. Additional Example 2: Using Scale Factors to Find Unknown Lengths 5151 Think: poster photo = l = l = 36 l = 7.2 Write a proportion to find the length l. Find the cross products. Divide.

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Holt CA Course 1 5-8Scale Drawings and Scale Models 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. Additional Example 2 Continued 5151 Think: poster photo = w = w = 20.5 w = 4.1 Write a proportion to find the width w. Find the cross products. Divide. The photo is 7.2 in. long and 4.1 in. wide.

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Holt CA Course 1 5-8Scale Drawings and Scale Models 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 Think: dollhouse blueprint = l = 45 · 1.5 l = 67.5 Write a proportion to find the length l. Find the cross products. Multiply. l 45 = 1.5 1

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Holt CA Course 1 5-8Scale Drawings and Scale Models Check It Out! 2 Continued w 24 = w = 24 · 1.5 w = 36 Write a proportion to find the width w. Find the cross products. Multiply. The dollhouse is 67.5 inches long and 36 inches wide. Think: dollhouse blueprint = 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

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Holt CA Course 1 5-8Scale Drawings and Scale Models 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? Additional Example 3: Measurement Application Let d be the actual distance between the cities = 7.5 d 1.5 · d = 60 · d = d 1.5 = d = 300 The distance between the cities is 300 miles. Write a proportion. Find the cross product. Multiply. Divide both sides by 1.5.

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Holt CA Course 1 5-8Scale Drawings and Scale Models 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 = 7d7d 1 · d = 50 · 7 1d = 350 d = 350 The distance between the cities is 350 kilometers. Write a proportion. Find the cross products. Multiply.

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