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Pre-Algebra 7-7 Scale Drawings 7-7 Scale Drawings Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Pre-Algebra 7-7 Scale Drawings Warm Up Evaluate the following for x = x2. x Evaluate the following for x = x4. x Pre-Algebra 7-7 Scale Drawings

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Pre-Algebra 7-7 Scale Drawings Problem of the Day An isosceles triangle with a base length of 6 cm and side lengths of 5 cm is dilated by a scale factor of 3. What is the area of the image? 108 cm 2

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Pre-Algebra 7-7 Scale Drawings Learn to make comparisons between and find dimensions of scale drawings and actual objects.

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Pre-Algebra 7-7 Scale Drawings Vocabulary scale drawing scale reduction enlargement

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Pre-Algebra 7-7 Scale Drawings A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar to the object. A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

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Pre-Algebra 7-7 Scale Drawings The scale a:b is read a to b. For example, the scale 1 cm:3 ft is read one centimeter to three feet. Reading Math ScaleInterpretation 1:201 unit on the drawing is 20 units. 1 cm: 1 m1 cm on the drawing is 1 m. in. = 1 ftin. on the drawing is 1 ft

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Pre-Algebra 7-7 Scale Drawings A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale? Additional Example 1A: Using Proportions to Find Unknown Scales or Lengths 1 cm x m = 2 cm 8 m Set up proportion using scale length. actual length 1 8 = x 2Find the cross products. 8 = 2x Solve the proportion. The scale is 1 cm:4 m. 4 = x

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Pre-Algebra 7-7 Scale Drawings B. The length of an object on a scale drawing is 1.5 inches. The scale is 1 in:6 ft. What is the actual length of the object? Additional Example 1B: Using Proportions to Find Unknown Scales or Lengths 1 in. 6 ft = 1.5 in. x ft Set up proportion using scale length. actual length 1 x = 6 1.5Find the cross products. x = 9Solve the proportion. The actual length is 9 ft.

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Pre-Algebra 7-7 Scale Drawings A. The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale? Try This: Example 1A 1 cm x m = 4 cm 12 m Set up proportion using scale length. actual length 1 12 = x 4Find the cross products. 12 = 4x Solve the proportion. The scale is 1 cm:3 m. 3 = x

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Pre-Algebra 7-7 Scale Drawings B. The length of an object on a scale drawing is 2 inches. The scale is 1 in:4 ft. What is the actual length of the object? Try This: Example 1B 1 in. 4 ft = 2 in. x ft Set up proportion using scale length. actual length 1 x = 4 2Find the cross products. x = 8Solve the proportion. The actual length is 8 ft.

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Pre-Algebra 7-7 Scale Drawings A scale drawing that is smaller than the actual object is called a reduction. A scale drawing can also be larger than the object. In this case, the drawing is referred to as an enlargement.

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Pre-Algebra 7-7 Scale Drawings Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? Additional Example 2: Life Sciences Application scale length actual length 1000 x = 1 8Find the cross products. x = The actual length of the amoeba is mm = 8 mm x mm Solve the proportion.

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Pre-Algebra 7-7 Scale Drawings Under a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length? Try This: Example 2 scale length actual length 10,000 x = 1 1Find the cross products. x = The actual length of the fiber is mm. 10,000 1 = 1 mm x mm Solve the proportion.

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Pre-Algebra 7-7 Scale Drawings A drawing that uses the scale in. = 1 ft is said to be in in. scale. Similarly, a drawing that uses the scale in. = 1 ft is in in. scale

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Pre-Algebra 7-7 Scale Drawings Additional Example 3A: Using Scales and Scale Drawings to Find Heights scale length actual length 0.25 x = 1 4 Find the cross products. x = 16 The wall is 16 ft tall in. 1 ft = 4 in. x ft. A. If a wall in a in. scale drawing is 4 in. tall, how tall is the actual wall? 1 4 Length ratios are equal. Solve the proportion.

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Pre-Algebra 7-7 Scale Drawings B. How tall is the wall if a in. scale is used? Additional Example 3B: Using Scales and Scale Drawings to Find Heights 1 2 scale length actual length 0.5 x = 1 4 Find the cross products. x = 8 The wall is 8 ft tall. 0.5 in. 1 ft = 4 in. x ft. Length ratios are equal. Solve the proportion.

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Pre-Algebra 7-7 Scale Drawings Try This: Example 3A scale length actual length 0.25 x = Find the cross products. x = 2 The wall is 2 ft thick in. 1 ft = 0.5 in. x ft. Length ratios are equal. Solve the proportion. A. If a wall in a in. scale drawing is 0.5 in. thick, how thick is the actual wall? 1 4

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Pre-Algebra 7-7 Scale Drawings B. How thick is the wall if a in. scale is used? Try This: Example 3A Continued 1 2 scale length actual length 0.5 x = Find the cross products. x = 1 The wall is 1 ft thick. 0.5 in. 1 ft = 0.5 in. x ft. Length ratios are equal. Solve the proportion.

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Pre-Algebra 7-7 Scale Drawings 1. What is the scale of a drawing in which a 9 ft wall is 6 cm long? 2. Using a in. = 1 ft scale, how long would a drawing of a 22 ft car be? 3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person? The scale of a map is 1 in. = 21 mi. Find each length on the map mi mi Lesson Quiz 1 4

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