1. Ratios and Proportions

2. 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?

3. 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.

4. 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)

5. An Easy Example
The ratio of the middle alien’s toes to fingers could be written as :
three-to-four
3:4

6. 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!)

7. Examples
Determine if the following ratios are proportional (equivalent fractions):
11 &
Cross multiply and compare products:
11 x 3 = 33
5 x 7 = 35

8. 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 ≠ 35
So &
are NOT proportional!

9. Use cross products to determine if the following ratios
Your turn:
Use cross products to determine if the following ratios
are proportional:
&

10. Answer (work shown!) Cross products are: 4 x 33 = 132 11 x 12 = 132
132 = 132, so they ARE proportional!

11. 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
Use cross products to solve for x:
13x = 3(52)
13x = 156
Divide both sides by 13:
X = 12

12. Use cross products to solve for h:
Your turn:
Use cross products to solve for h:
20 = h

13. Pretty easy, right?!?
Answer:
28h = 20(21)
28h = 420
h = 15

14. 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?

15. 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_

16. Cross Multiply & Divide:
5u = 7(2280)
5u = 15960
u = 3192