Ratios and Proportions

Chapter 3 Section 6

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?

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.

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)

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

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!)

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

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!

Your turn:

Use cross products to determine if the following ratios are proportional:

4 & 12 11 33

Answer (work shown!)

Cross products are:

4 x 33 = 132

11 x 12 = 132

132 = 132, so they ARE proportional!

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

Your turn:

Use cross products to solve for h:

20 = h

28 21

Pretty easy, right?!?Answer:

28h = 20(21)

28h = 420

28 28

h = 15

What happens if there are DECIMALS in the

problem?!?!

USE YOUR CALCULATOR

USE CROSS PRODUCTS

GET THE ANSWER!

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?

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

Cross Multiply & Divide:

7 = _u_

5 2280

5u = 7(2280)

5u = 15960

5 5

u = 3192

Assignment:

Worksheet 3-62 sides!!

The End!