Download - Ratios And Proportions
![Page 1: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/1.jpg)
Ratios and Proportions
Chapter 3 Section 6
![Page 2: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/2.jpg)
Hmmmmm…… It was recently estimated by the Extraterrestrial
Alien Monitoring Agency that unregistered extraterrestrials outnumber registered ones by about seven-to-five. If there are a total of 2,280 registered extraterrestrials, about how many are unregistered?
![Page 3: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/3.jpg)
Ratios
The expression seven-to-five is a ratio. It describes a size comparison between two things…..in this case, the number of registered aliens to unregistered ones.
![Page 4: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/4.jpg)
Ways of expressing them….
• Ratios can be expressed with words, such as in the alien problem (seven-to-five)
• Ratios can be expressed with a colon (7:5)
• Ratios can be expressed as a fraction (7/5)
![Page 5: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/5.jpg)
An Easy Example
The ratio of the middle alien’s toes to fingers could be written as :
1. three-to-four
2. 3:4
3. ¾
![Page 6: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/6.jpg)
Cross Products (to determine proportions)
Two ratios can be proved equivalent (or Proportional) by using cross products:
(This is the ONLY time you will be able to CROSS MULTIPLY, so enjoy!)
![Page 7: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/7.jpg)
ExamplesDetermine if the following
ratios are proportional (equivalent fractions):
11 & 7 5 3
Cross multiply and compare products:
11 x 3 = 335 x 7 = 35
![Page 8: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/8.jpg)
How did the products compare?
If the products are equal, then the ratios are proportional.If the products are not equal, then the ratios are not proportional.
33 ≠ 35So 11 & 7 5 3 are NOT proportional!
![Page 9: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/9.jpg)
Your turn:
Use cross products to determine if the following ratios are proportional:
4 & 12 11 33
![Page 10: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/10.jpg)
Answer (work shown!)
Cross products are:
4 x 33 = 132
11 x 12 = 132
132 = 132, so they ARE proportional!
![Page 11: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/11.jpg)
Unknown values in a Proportion:
Sometimes you will be given a proportion (equal fractions) with an unknown value to solve for, such as the following:
3 = x 13
52
Use cross products to solve for x:
13x = 3(52)
13x = 156 Divide both
sides by 13:
X = 12
![Page 12: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/12.jpg)
Your turn:
Use cross products to solve for h:
20 = h
28 21
![Page 13: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/13.jpg)
Pretty easy, right?!?Answer:
28h = 20(21)
28h = 420
28 28
h = 15
![Page 14: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/14.jpg)
What happens if there are DECIMALS in the
problem?!?!
USE YOUR CALCULATOR
USE CROSS PRODUCTS
GET THE ANSWER!
![Page 15: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/15.jpg)
Now, solve the alien problem using ratios /
proportions:It was recently estimated by the Extraterrestrial
Alien Monitoring Agency that unregistered extraterrestrials outnumber registered ones by about seven-to-five. If there are a total of 2,280 registered extraterrestrials, about how many are unregistered?
![Page 16: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/16.jpg)
Set-Up:• The given ratio is seven-to-five
(unregistered to registered)
• The other given amount is 2,280 registered
• The unknown amount is for unregistered
7 = _u_
5 2280
![Page 17: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/17.jpg)
Cross Multiply & Divide:
7 = _u_
5 2280
5u = 7(2280)
5u = 15960
5 5
u = 3192
![Page 18: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/18.jpg)
Assignment:
Worksheet 3-62 sides!!
![Page 19: Ratios And Proportions](https://reader035.vdocuments.us/reader035/viewer/2022081421/55506a56b4c90524138b46c6/html5/thumbnails/19.jpg)
The End!