Ratios And Proportions

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Algebra 1 tutorial

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Ratios And Proportions

  1. 1. Ratios and Proportions Chapter 3 Section 6
  2. 2. Hmmmmm…… <ul><li>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? </li></ul>
  3. 3. Ratios <ul><li>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. </li></ul>
  4. 4. Ways of expressing them…. <ul><li>Ratios can be expressed with words, such as in the alien problem (seven-to-five) </li></ul><ul><li>Ratios can be expressed with a colon (7:5) </li></ul><ul><li>Ratios can be expressed as a fraction (7/5) </li></ul>
  5. 5. An Easy Example <ul><li>The ratio of the middle alien’s toes to fingers could be written as : </li></ul><ul><li>three-to-four </li></ul><ul><li>3:4 </li></ul><ul><li>¾ </li></ul>
  6. 6. Cross Products (to determine proportions) <ul><li>Two ratios can be proved equivalent (or Proportional) by using cross products: </li></ul><ul><li>(This is the ONLY time you will be able to CROSS MULTIPLY, so enjoy!) </li></ul>
  7. 7. Examples <ul><li>Determine if the following ratios are proportional (equivalent fractions): </li></ul><ul><li>11 & 7 </li></ul><ul><li>5 3 </li></ul><ul><li>Cross multiply and compare products: </li></ul><ul><li>11 x 3 = 33 </li></ul><ul><li>5 x 7 = 35 </li></ul>
  8. 8. How did the products compare? <ul><li>If the products are equal , </li></ul><ul><li>then the ratios are proportional. </li></ul><ul><li>If the products are not equal , </li></ul><ul><li>then the ratios are not proportional . </li></ul><ul><li>33 ≠ 35 </li></ul><ul><li>So 11 & 7 </li></ul><ul><li>5 3 are NOT proportional! </li></ul>
  9. 9. Your turn: <ul><li>Use cross products to determine if the following ratios </li></ul><ul><li>are proportional: </li></ul><ul><li>4 & 12 </li></ul><ul><li>11 33 </li></ul>
  10. 10. Answer (work shown!) <ul><li>Cross products are: </li></ul><ul><li>4 x 33 = 132 </li></ul><ul><li>11 x 12 = 132 </li></ul><ul><li>132 = 132, so they ARE proportional! </li></ul>
  11. 11. Unknown values in a Proportion: <ul><li>Sometimes you will be given a proportion (equal fractions) with an unknown value to solve for, such as the following: </li></ul><ul><li>3 = x </li></ul><ul><li>13 52 </li></ul><ul><li>Use cross products to solve for x: </li></ul><ul><li>13x = 3(52) </li></ul><ul><li>13x = 156 </li></ul><ul><li>Divide both sides by 13: </li></ul><ul><li>X = 12 </li></ul>
  12. 12. Your turn: <ul><li>Use cross products to solve for h: </li></ul><ul><li>20 = h </li></ul><ul><li>28 21 </li></ul>
  13. 13. Pretty easy, right?!? <ul><li>Answer: </li></ul><ul><li>28h = 20(21) </li></ul><ul><li>28 h = 420 </li></ul><ul><li>28 28 </li></ul><ul><li>h = 15 </li></ul>
  14. 14. What happens if there are DECIMALS in the problem?!?! <ul><li>USE YOUR CALCULATOR </li></ul><ul><li>USE CROSS PRODUCTS </li></ul><ul><li>GET THE ANSWER! </li></ul>
  15. 15. Now, solve the alien problem using ratios / proportions: <ul><li>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? </li></ul>
  16. 16. Set-Up: <ul><li>The given ratio is seven-to-five (unregistered to registered) </li></ul><ul><li>The other given amount is 2,280 registered </li></ul><ul><li>The unknown amount is for unregistered </li></ul><ul><li>7 = _ u_ </li></ul><ul><li>5 2280 </li></ul>
  17. 17. Cross Multiply & Divide: <ul><li>7 = _ u_ </li></ul><ul><li>5 2280 </li></ul><ul><li>5u = 7(2280) </li></ul><ul><li>5 u = 15960 </li></ul><ul><li>5 5 </li></ul><ul><li>u = 3192 </li></ul>
  18. 18. Assignment: <ul><li>Worksheet 3-6 </li></ul><ul><li>2 sides!! </li></ul>
  19. 19. The End!

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