6.2 Proportions

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Chapter 6, Section 2: Proportions

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6.2 Proportions

  1. 1. <ul><li>What are the three ways of writing a ratio? </li></ul><ul><li>I drove 489 miles from San Diego to San Jose, California. I had a full tank of 16 gallons of gas in my tank when I left San Diego. I now have ¼ of a tank left. How many miles to 1 gallon did drive? </li></ul>Warm Up:
  2. 2. Chapter 6: Ratios, Proportions, and Percents And you thought fractions where a pain. Section 2: Proportions
  3. 3. Proportion <ul><li>An Equality of TWO Ratios. </li></ul><ul><li>For Example: 6/9 = 8/12 </li></ul><ul><li>The ratios are equivalent. </li></ul><ul><li>Which means they reduce to the same fraction in it’s simplest form! </li></ul>
  4. 4. Try This On For Size…a/b = c/d <ul><li>Multiplication Property of Equality (Method 1) (get the denominators to be the same  what is done to the bottom is done to the top) </li></ul><ul><li>b/b = 1 and d/d = 1 ( cancel out stuff on the top and bottom that are the same) </li></ul><ul><li>ad and bc are called the Cross Products of the proportion a/b = c/d. </li></ul>
  5. 5. <ul><li>PROOF OF PROPORTIONS: </li></ul><ul><li>Multiplication Property of Equality! </li></ul><ul><li> If a/b = c/d </li></ul><ul><li>Simplify </li></ul><ul><li>Get Common Denominators and Multiply TOP and BOTTOM. </li></ul><ul><li>Then Cancel! </li></ul>
  6. 6. Cross Product: The Easy Way (Method 2) <ul><li>In a proportion, the cross products of the two ratios are equal! </li></ul><ul><li>Arithmetic: 6 / 9 = 8 / 12 if, 6 • 12 = 9 • 8 </li></ul><ul><li> 72 = 72 </li></ul><ul><li>Algebra: a / b = c / d if, a • d = c • b </li></ul><ul><li>ad = cb </li></ul><ul><li>You can use Cross Product to find variables in proportions to make the proportions true. </li></ul>
  7. 7. Try the Two Ways to Find Variables in Proportions: X/9 = 4/6 <ul><li>Method 1: Multiplication Property of Equality. (Common Denominator) </li></ul><ul><li>Method 2: Cross Product. (Cross Multiply) </li></ul>
  8. 8. Solve Using Your Favorite Method <ul><li>H/9 = 2/3 </li></ul><ul><li>22/D = 6/21 </li></ul>
  9. 9. Do the two Ratios form a Proportion? <ul><li>Two ratios form a proportion if the cross product are equal. </li></ul><ul><li>Tell me whether each pair of ratios form a proportion by your Favorite Method. </li></ul><ul><li>15/20 and 5/7 Yes or No? </li></ul><ul><li>7/12 and 17.5/30 Yes or No? </li></ul>
  10. 10. You Can Use Proportions to Solve Word/World Problems <ul><li>One hundred nautical miles equals about 115 standard, or statue, miles. To the nearest mile, how far in statue miles is 156 nautical miles? </li></ul><ul><li>Let d = distance in statue miles. </li></ul><ul><li>100/115 = 156/d </li></ul><ul><li>100d = 115(156) </li></ul><ul><li>d = 179 </li></ul>Proportion  two ratios that are equal. Written as Cross Product Divide Each Side by 100. 156 nautical miles is about 179 statue miles.
  11. 11. Assignment #43 <ul><li>Page 286-287 : 18-29 All , 38-45 All , 53 , and 55 . </li></ul><ul><li>MAKE SURE YOU WRITE THIS DOWN CORRECTLY!!! </li></ul>

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