Scale Drawings & Scale Factor

Ratio Proportion 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

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.

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.

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

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

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.

Practice Problems

A set of landscape plans shows a flower bed that is 6. 5 inches wide 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?

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?

A set of landscape plans shows a flower bed that is 6. 5 inches wide 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

What is the scale factor? 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

The Percent Proportion

Cross multiply to get the answer. 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.

Percent Proportion part percent a p = = base 100 b 100 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

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

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

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

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

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

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

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)

Homework Page 16, #1-2 Page 18, #7-11 Page 19-20, #13-17, 19