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# Ratiosandpropday1 2014

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### Transcript

• 1. 7-1 Ratio and Proportion Objectives Write and simplify ratios. Use proportions to solve problems. Holt McDougal Geometry
• 2. 7-1 Ratio and Proportion Vocabulary ratio proportion extremes means cross products Holt McDougal Geometry
• 3. 7-1 Ratio and Proportion A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b, a:b, or , where b ≠ 0. For example, the ratios 1 to 2, 1:2, and all represent the same comparison. Holt McDougal Geometry
• 4. 7-1 Ratio and Proportion Remember! In a ratio, the denominator of the fraction cannot be zero because division by zero is undefined. Holt McDougal Geometry
• 5. 7-1 Ratio and Proportion A proportion is an equation stating that two ratios are equal. In the proportion , the values a and d are the extremes. The values b and c are the means. When the proportion is written as a:b = c:d, the extremes are in the first and last positions. The means are in the two middle positions. Holt McDougal Geometry
• 6. PROPORTION TWO EQUAL RATIOS a = c b d MEANS: b,c EXTREMES: a,d
• 7. Use the proportion given to complete each statement a. 5 y b. x 5 y 2 x y y c. 2 5 ? ? d. ? ? x ? 5 ?
• 8. Cross Products Property The product of the means equals the product of the extremes.
• 9. Properties of Proportions a c = b d 1. ad = bc
• 10. PROPERTIES OF PROPORTION Exchange Property You may exchange the means or the extremes.
• 11. Properties of Proportions a c = b d a c = b d
• 12. PROPERTIES OF PROPORTION Reciprocal Property Take the reciprocal of both ratios.
• 13. Properties of Proportions a c = b d b a = d c
• 14. PROPERTIES OF PROPORTION “Add One” Property
• 15. Properties of Proportions a c = b d a+b b = c+d d
• 16. 7-1 Ratio and Proportion Example 3A: Solving Proportions Solve the proportion. 7(72) = x(56) 504 = 56x x=9 Holt McDougal Geometry Cross Products Property Simplify. Divide both sides by 56.
• 17. 7-1 Ratio and Proportion Example 3B: Solving Proportions Solve the proportion. (z – 4)2 = 5(20) Cross Products Property (z – 4)2 = 100 Simplify. (z – 4) = 10 Find the square root of both sides. (z – 4) = 10 or (z – 4) = –10 Rewrite as two eqns. z = 14 or z = –6 Holt McDougal Geometry Add 4 to both sides.
• 18. 7-1 Ratio and Proportion Check It Out! Example 3a Solve the proportion. 3(56) = 8(x) 168 = 8x x = 21 Holt McDougal Geometry Cross Products Property Simplify. Divide both sides by 8.
• 19. 7-1 Ratio and Proportion Check It Out! Example 3b Solve the proportion. 2y(4y) = 9(8) 8y2 = 72 Cross Products Property Simplify. y2 = 9 Divide both sides by 8. y= 3 Find the square root of both sides. y = 3 or y = –3 Holt McDougal Geometry Rewrite as two equations.
• 20. 7-1 Ratio and Proportion Check It Out! Example 3c Solve the proportion. d(2) = 3(6) 2d = 18 d=9 Holt McDougal Geometry Cross Products Property Simplify. Divide both sides by 2.
• 21. 7-1 Ratio and Proportion Check It Out! Example 3d Solve the proportion. (x + 3)2 = 4(9) Cross Products Property (x + 3)2 = 36 Simplify. (x + 3) = 6 Find the square root of both sides. (x + 3) = 6 or (x + 3) = –6 Rewrite as two eqns. x = 3 or x = –9 Holt McDougal Geometry Subtract 3 from both sides.
• 22. 7-1 Ratio and Proportion ? Holt McDougal Geometry ? ?