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Ratios and Proportions {BASICS}

Learn about ratios and proportions through an intriguing alien estimation scenario. Practice cross-multiplying and solving proportions with this educational guide.

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Ratios and Proportions {BASICS}

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  1. Ratios and Proportions{BASICS} Dr. Joseph Domenech

  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 • ¾

  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 & 7 5 3 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 11 & 7 5 3 are NOT proportional!

  9. Your turn: Use cross products to determine if the following ratios are proportional: 4 & 12 11 33

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

  11. 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 Unknown values in a Proportion:

  12. Your turn: Use cross products to solve for h: 20 = h 28 21

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

  14. What happens if there are DECIMALS in the problem?!?! USE YOUR CALCULATOR USE CROSS PRODUCTS GET THE ANSWER!

  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?

  16. 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

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

  18. Assignment: Worksheet 3-6 2 sides!!

  19. The End!

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