1. LESSON 8.1: RATIOS AND PROPORTIONS
OBJECTIVE: To write ratios and solve proportions
Mrs. McConaughy Geometry

2. Mrs. McConaughy Geometry
Definition: Ratio
an expression that
A ratio is ____________________
____________________________.
If a and b are two numbers, the ratio of a to b can be written in the following ways:
compares two quantities by division
a/b a:b a is to b
Mrs. McConaughy Geometry

3. Mrs. McConaughy Geometry
FINDING RATIOS:
Determine the following ratios:
female to male students
in this classroom ____
male to female students
male to total students
total students to female
students in this
classroom ____
Mrs. McConaughy Geometry

4. Mrs. McConaughy Geometry
FINDING RATIOS:
Determine the following ratios:
Ratio of ♥ to ♣:__
♥♣♥♣♥♣♥♣♥♣♥♣♥♣♣
♣♣♣♥♥♣♣♣♥♥♣♣♣♥♥
♣♥♣♣♣♥♣♣♣♥♣♣♥♥♥
♥♥♥♣♣♥♥♥♥♥♥♣♣♥♥♥
Ratio of shaded to unshaded area:__
Ratio of shaded area to area of the whole figure:__
Mrs. McConaughy Geometry

5. Mrs. McConaughy Geometry
Example
A scale model of a car is 4 inches long. The actual car is 15 ft. long.
a.) What is the ratio of the length of the model to the length of the car? ________________
b.) What is the ratio of the length of the car to the length of the model? ______________
Write both measurements in the same units.
NOTE: ORDER is
important
when writing ratios.
Mrs. McConaughy Geometry

6. Mrs. McConaughy Geometry
Example
A photo that is 8 inches wide and 5 1/3 inches high is enlarged to poster size which is 2 ft. wide by 1 1/3 ft. high.
What is the ratio of the height of the photo to the height of the poster? .
NOTE: ORDER is
important
when writing ratios.
Mrs. McConaughy Geometry

7. Mrs. McConaughy Geometry
Proportion
When two ratios are equal, you have
a ________.
proportion
Mrs. McConaughy Geometry

8. Mrs. McConaughy Geometry
Proportion
a statement of equality between two ratios (equal ratios).
A proportion is___________ _______________________
_______________________.
extremes
a : b = c : d
means
Mrs. McConaughy Geometry

9. Mrs. McConaughy Geometry
PROPERTIES OF PROPORTIONS
1. Cross Product Property The product of the extremes equals the product of the means.
If a = c, then________.
b d
2. Reciprocal Property If two ratios are equal, then their reciprocals are also equal.
If a = c, then
b d __________.
ad = bc
b = d
a c
Mrs. McConaughy Geometry

10. To solve the proportion, you find the value of the variable.
Solve the proportions.
a. 4 = b = 2
x y y
Mrs. McConaughy Geometry

11. Example Solving for a Variable
Before you cross multiply, determine if you can reduce fractions.
Example: 26 = __ 50 13 25
How can you determine the answer
without cross multiplying?
Mrs. McConaughy Geometry

12. Additional Properties of Proportions
Two more properties of proportions, which are especially useful in geometry, are: b d
c + d d
Mrs. McConaughy Geometry

13. Mrs. McConaughy Geometry
NOTE: You can avoid memorizing
many of the Properties of
Proportions by remembering to
write your ratio (comparison of two
quantities by division) in words
before setting up and solving your
proportion by cross multiplying.
ORDER is
important
when setting
up proportions.
Mrs. McConaughy Geometry

14. Mrs. McConaughy Geometry
Complete:
The Cross-Product Property states that________________.
Mrs. McConaughy Geometry

15. Mrs. McConaughy Geometry
Solving for a Variable
3x = 2 (x + 1)
3x = 2x + 2
x = 2
Mrs. McConaughy Geometry

16. Mrs. McConaughy Geometry
USING PROPORTIONS
If you earn $380 working for two weeks, how much will you earn in 15 weeks?
KEY: Words  Symbols
Always remember to set up your proportion in words first!
Mrs. McConaughy Geometry

17. Mrs. McConaughy Geometry
Example: (Always ask: What two quantities am I comparing?) x x
Mrs. McConaughy Geometry

18. Mrs. McConaughy Geometry
2x = (380)(15)
2x = 5700
x = 2850
You will earn $2,850 in 15 weeks.
Mrs. McConaughy Geometry

19. Mrs. McConaughy Geometry
Extended Proportions
An extended proportion is _______________________.
Mrs. McConaughy Geometry

20. Mrs. McConaughy Geometry
USING PROPORTIONS
The floor plan of a house is drawn
to the scale of ¼ inch = 1 foot. The
master bedroom measures 3 inches
by 3 ¾ inches on the blueprints.
What are the actual measurements
of the room?
Mrs. McConaughy Geometry

21. The actual size of the room is_______________ . 12 feet by 15 feet
Pick your poison: Choose how you want to set up your two ratios in words first!
NOTE: Rather than writing an extended proportion,
you may find it easier to write two separate proportions.
Mrs. McConaughy Geometry

22. Final Checks for Understanding
1. A ratio is_______________________.
2. A proportion is ___________________.
3. What is the most efficient way to solve
8 = x ? Explain.
24 9
4. Solve for x: 4 = x
x 16.
Mrs. McConaughy Geometry

23. Summary: Properties of Proportionsd c ac b d
c + d d
Mrs. McConaughy Geometry

24. Mrs. McConaughy Geometry
Homework Assignment:
Ratios and Proportions WS
Mrs. McConaughy Geometry