1. Scale Drawings & Scale Factor

2. Ratio Proportion 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 proportional to 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
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
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. 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

14. The Percent Proportion

15. 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.

16. 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

17. 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.

18. 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

19. 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.

20. 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

21. 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.

22. 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

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