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Proportions and Ratios

Proportions and Ratios. by Kylan Parayao. Vocabulary and Examples . Ratio : A comparison of two numbers or quantities Numerical Example : 1 apple : 3 oranges This ratio compares apples to oranges. It means for every apple there are 3 oranges. Algebraic Example: A /B

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Proportions and Ratios

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  1. Proportions and Ratios by Kylan Parayao

  2. Vocabulary and Examples • Ratio: A comparison of two numbers or quantities Numerical Example:1 apple : 3 oranges This ratio compares apples to oranges. It means for every apple there are 3 oranges. Algebraic Example:A/B • Proportions: Is an algebraequation that states two ratios are equal Numerical Example:1/2 = 2/4 2 * 2 = 1 * 4 4 = 4 Algebraic Example:1/2 = x/6 x * 2 = 1 * 6 2x = 6 x = 3

  3. Vocabulary and Examples continued • Extremes: the numbers that are located on the top left and the bottom right of the equation. • Means: the numbers that are located on the top right and the bottom left. Source: http://www.algebrahelp.com/lessons/proportionbasics/index.htm

  4. Necessary Prior Knowledge • Cross products property • Cross Products is a method of checking proportions to see if the the two ratios are equal, which would make the sentence correct. • For Example: 4 feet/8 people = 12 feet/p people. • Source: http://eclass1.wsd.k12.ca.us/moodle/mod/resource/view.php?id=481

  5. Main Ideas • A proportion is a comparison of two ratios that are often in fraction form. • A ratio is a comparison between two values. • Cross products are a method of checking to see if the two proportions are equal.

  6. Formulas and examples • Ratio: • A:B or A/B • 1 apple:3 oranges • 1 apple/3 oranges • Proportion: • A/B = C/D • 1/2 = x/6 • Cross Products: • A/B = C/D • A*D = B*C

  7. Example Problems • Problem 1 • Jane has a box of apples and oranges in the ratio of 2:3. If she has six apples, how many oranges does she have? • Problem 2 • Solve for x: • x students/6 teachers = 209 students/11 teachers

  8. Answers • Problem 1 • Jane has a box of apples and oranges in the ratio of 2:3. If she has six apples, how many oranges does she have? • Answer: 2 apples/3 oranges = 6 apples/x oranges 2*x = 6*3;2x = 18; x = 9 9 oranges • Problem 2 • Solve for x: • x students/6 teachers = 209 students/11 teachers • Answer: x*11 = 209*6; 11x = 1254; x = 114 114 students

  9. References • Class Notes: Unit 2, Concept:Proportions Date:9/22/12 • Internet Resources: • http://www.algebrahelp.com/lessons/proportionbasics/index.htm • http://eclass1.wsd.k12.ca.us/moodle/mod/resource/view.php?id=481

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