![Page 1: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/1.jpg)
Mrs. McConaughy Geometry 1
LESSON 8.1: RATIOS AND PROPORTIONS
OBJECTIVE:OBJECTIVE: To write ratios and solve proportions
![Page 2: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/2.jpg)
Mrs. McConaughy Geometry 2
Definition:: Ratio
A ratio is ________________________________________________. If a and b are two numbers, the
ratio of a to b can be written in the following ways:
a/b a:b a is to b
an expression thatcompares two quantities by division
![Page 3: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/3.jpg)
Mrs. McConaughy Geometry 3
FINDING RATIOS:Determine the following ratios:
female to male studentsin this classroom ____
male to female studentsin this classroom ____
male to total studentsin this classroom ____
total students to femalestudents in this classroom ____
![Page 4: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/4.jpg)
Mrs. McConaughy Geometry 4
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:__
![Page 5: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/5.jpg)
Mrs. McConaughy Geometry 5
ExampleA 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.
![Page 6: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/6.jpg)
Mrs. McConaughy Geometry 6
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.
![Page 7: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/7.jpg)
Mrs. McConaughy Geometry 7
ProportionProportion When two ratios are equal, you have
a ________.
.3 6= is a proportion4 8
proportion
![Page 8: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/8.jpg)
Mrs. McConaughy Geometry 8
Proportion
A proportion is__________________________________
_______________________.
a statement of equality between two ratios (equal ratios).
a c = and a: b = c:d are examples of proportions b d
a : b = c : d extremes
means
![Page 9: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/9.jpg)
Mrs. McConaughy Geometry 9
PROPERTIES OF PROPORTIONS1. Cross Product Property The product of the extremes equals the product of the means.
If a = c, then________. b d2. 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
![Page 10: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/10.jpg)
Mrs. McConaughy Geometry 10
To solve the proportion, you find the value of the variable.
Solve the proportions. a. 4 = 5 b. 3 = 2 x 7 y +2 y
![Page 11: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/11.jpg)
Mrs. McConaughy Geometry 11
Example Solving for a Variable
26 xSolve f or x in = 50 75.
Before you cross multiply, determine if you can reduce fractions. Example: 26 = __ 50
13
25
13 x= 25 75
How can you determine the answer without cross multiplying?
![Page 12: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/12.jpg)
Mrs. McConaughy Geometry 12
Additional Properties of Proportions
Two more properties of proportions, which are especially useful in geometry, are:
c
a cI f is equivalent tob d
a a + b = _____ and = _____b
b
d
c + d
d
![Page 13: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/13.jpg)
Mrs. McConaughy Geometry 13
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.
![Page 14: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/14.jpg)
Mrs. McConaughy Geometry 14
Complete:
.a 12 bI f = , then =4 b 12
Write two expressions that m nare equivalent to = 4 11.
The Cross-Product Property states that________________.
![Page 15: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/15.jpg)
Mrs. McConaughy Geometry 15
Solving for a Variable
x + 1 xSolve f or x in = 3 2
3x = 2 (x + 1)
3x = 2x + 2
x = 2
![Page 16: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/16.jpg)
Mrs. McConaughy Geometry 16
USING PROPORTIONS If you earn $380 working for two
weeks, how much will you earn in 15 weeks?
KEY: Words SymbolsAlways remember to set up your proportion in words first!
![Page 17: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/17.jpg)
Mrs. McConaughy Geometry 17
Example: (Always ask: What two quantities am I comparing?)
money = weeks
weeks _______ = _______money
380 x
2 15
2 15
380 x
![Page 18: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/18.jpg)
Mrs. McConaughy Geometry 18
2x = (380)(15) 2x = 5700 x = 2850
You will earn $2,850 in 15 weeks.
![Page 19: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/19.jpg)
Mrs. McConaughy Geometry 19
.
6 4 1 = = is an example of an24 16 4 extended proportion
Extended Proportions
An extended proportion is _______________________.
![Page 20: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/20.jpg)
Mrs. McConaughy Geometry 20
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?
USING PROPORTIONS
![Page 21: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/21.jpg)
Mrs. McConaughy Geometry 21
f eetinches =
f eet _______ = _______inches
The actual size of the room is_______________ .12 feet by 15 feet
NOTE: Rather than writing an extended proportion, you may find it easier to write two separate proportions.
Pick your poison: Choose how you want to set up your two ratios in words first!
![Page 22: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/22.jpg)
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 94. Solve for x: 4 = x x 16.
![Page 23: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/23.jpg)
Mrs. McConaughy Geometry 23
Summary: Properties of Proportions
a c= is equivalent tob d
b(1) ad = _____ (2) = _____aa a + b (3) = ___ (4) = ____c b
ac
d
c
b
d
c + d
d
![Page 24: Mrs. McConaughy Geometry1 LESSON 8.1: RATIOS AND PROPORTIONS OBJECTIVE: OBJECTIVE: To write ratios and solve proportions](https://reader034.vdocuments.mx/reader034/viewer/2022042502/56649d765503460f94a5707e/html5/thumbnails/24.jpg)
Mrs. McConaughy Geometry 24
Homework Assignment:
Ratios and Proportions WS