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Lesson 6.5 Scale Drawings Students will be able to understand ratios and proportions in scale drawings.

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**Write each fraction in the simplest form.**

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

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**This HO gauge model train is a scale model of a historic train**

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. (1 inch on the model is 87 inches on the actual train.)

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**A scale is the ratio between two sets of measurements**

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 drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

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**Write a ratio using one of the dimensions**

Identify the scale factor. Room Blueprint Length 12 ft. 18 in. Width 9 ft. 13.5 in. Write a ratio using one of the dimensions Blueprint Length Room Length 18 in. 12 ft. = Units are like quantities (length to length). They must be converted to common units! Which unit will you convert? FEET to INCHES 12 ft x _____ 12 1 in. = 144 in. Now replace 12ft with 144 in. 1 ft. 18 18 Simplify. (Scale factor ratios must be written as a single unit rate) 18 in. 144 in. = Remember from lesson 6.1 when common units (in.) are used the ratio will NOT have units! 1 8 The scale factor is:

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**First: Write a ratio using one of the dimensions**

Identify Scale Factor: Your Turn! Room Blueprint Length 8 ft. 1 in. Width 18 ft. 2.25 in. First: Write a ratio using one of the dimensions Blueprint width Room width or 2.25 in. 18 ft. Blueprint length Room length Units are like quantities (length to length). They must be converted to common units! Which unit will you convert? or Room width Blueprint width FEET to INCHES 18 ft. x _________ 12 1 in. ft. = 216 in. 1 Simplify. (Scale factor ratios must be written as a single unit rate) 2.25 in. 216 in. 2.25 1 96 = 1 96 The scale factor is:

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**: : = = 300 = x Measurement Application**

On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles? Write a proportion Pittsburgh to Philadelphia (map) Pittsburgh to Philadelphia (actual) = Scale (map) Scale (actual) Substitute Values 7.5 in. X miles = 1.5 in. 60 miles Cross Products 7.5 x 60 = 1.5x : : Divide Both sides by 1.5 450 = 1.5x 300 = x The distance between the cities is 300 miles.

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**= = 2.5in. 3 in. 1 in. = 2 ft. = 1in scale 2ft scale**

Use the scale on the drawing to find the scale factor and the perimeter of the tree house. 1 24 Convert to same units for scale factor. 1 in. 2ft. In. The scale is: = 1 24 2 ft. x 12 in. ft. = 24 in Scale factor = Perimeter of Drawing Actual object 1in scale 2ft scale Write a proportion to find the perimeter of the actual object. = 2.5in. 3 in. 11 in. x ft. 1 in. 2 ft. Substitute. = 1 in. = 2 ft. Use cross products. 11 x 2 = 1x 22 = x The actual perimeter of the tree house is 22 ft.

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Homework Time: Page 287 problems 1-16 all

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