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Scale Drawings & Scale Factor

Scale Drawings & Scale Factor. Ratio. A ratio is a comparison of two quantities A proportion states that two ratios (or fractions) are equal. Proportion. Scale. A scale is a ratio between two sets of measurements. Examples: Drawings: ¼ inch = 1 foot Maps: 1 inch = 250 miles.

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Scale Drawings & Scale Factor

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  1. Scale Drawings & Scale Factor

  2. Ratio • A ratio is a comparison of two quantities • A proportion states that two ratios (or fractions) are equal Proportion

  3. Scale • A scale is a ratio between two sets of measurements. • Examples: • Drawings: ¼ inch = 1 foot • Maps: 1 inch = 250 miles

  4. Scale Drawings (continued) • The scale is shown as the length in the drawing, then a colon (":"), then the matching length on the real thing. • Example: the drawing below has a scale of "1:10", so anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 150mm on the drawing would be 1500mm on the real horse.

  5. Scale Drawing (Model) • A scale drawing (model) is a drawing that uses a scale to make an object smaller than (reduction) or larger than (enlargement) the real object.

  6. Scale Factor • A scale factor is a ratio used to enlarge or reduce similar figures. • Examples: If the scale factor is 2 for a 16 ft. figure, the image will then be 2x16 = 32 ft

  7. The lengths and widths of objects of a scale drawing or model are proportionalto the lengths and widths of the actual object.

  8. Even More Vocab • Corresponding sides - a pair of matching sides that are in the same spot in two different shapes. • Corresponding Angles – a pair of matching angles that are in the same spot in two different shapes.

  9. Practice Problems

  10. A set of landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4 feet. • What is the width of the actual flower bed? • What is the scale factor?

  11. The central chamber of the Lincoln memorial, which features a marble statue of Abraham Lincoln, has a height of 60 feet. Suppose a scale model of the chamber has a height of 4 inches. What is the scale of the model? • Write a ratio of the height of the model to the actual height of the statue? • What is the scale factor?

  12. A set of landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4 feet. • What is the width of the actual flower bed? • What is the scale factor? 26 feet 1/48

  13. The central chamber of the Lincoln memorial, which features a marble statue of Abraham Lincoln, has a height of 60 feet. Suppose a scale model of the chamber has a height of 4 inches. What is the scale of the model? • Write a ratio of the height of the model to the actual height of the statue? • What is the scale factor? 60ft 4in 15ft 1in 1 inch = 15 feet 1/180

  14. The Percent Proportion

  15. = What is 175% of 80? Use the proportion. x 175 80 100 x = 140 140 is 175% of 80 Cross multiply to get the answer.

  16. Percent Proportion • Compares part of a quantity to the whole quantity, called the base, using a percent. • The percent proportion is: part percent a p = = base 100 b 100

  17. Percent Proportion • What percent of $15 is $9? The part. The percent is the unknown. The base always follows the word of.

  18. Percent Proportion. • What percent of $15 is $9? p 9 = Cross multiply. 15 100 15p = 900 p = 60 So 60% of $15 is $9. 15 15

  19. Percent Proportion • What number is 30% of 150? The percent. The part is the unknown. The base always follows the word of.

  20. Percent Proportion. • What number is 30% of 150? 30 a = Cross multiply. 150 100 100a = 4500 a = 45 So 45 is 30% of 150. 100 100

  21. Percent Proportion • 12 is 80% of what number? The base is the unknown. The base always follows the word of. The percent. The part.

  22. Percent Proportion. • 12 is 80% of what number? 80 12 = Cross multiply. b 100 80b = 1200 b = 15 So 12 is 80% of 15. 80 80

  23. Finding Percentages of Enlargement/Reductions • To find the percentage of an enlargement or reduction, we must take two corresponding sides and make a proportion Ex: (do on whiteboard)

  24. Homework66 • Page 16, #1-2 • Page 18, #6-11 • Page 19-20, #13-17, 19 • Page 21, #20, 21

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