Ratios and Proportions

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Presentation transcript:

Ratios and Proportions

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 : three-to-four 3:4 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!)

Examples Determine if the following ratios are proportional (equivalent fractions): 11 & 7 5 3 Cross multiply and compare products: 11 x 3 = 33 5 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 ≠ 35 So 11 & 7 5 3 are NOT proportional!

Use cross products to determine if the following ratios 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

Use cross products to solve for h: 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

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: 5 2280 5u = 7(2280) 5u = 15960 5 5 u = 3192