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Solve Proportions and Identify Means and Extremes in Mathematical Equations

This guide provides step-by-step procedures for solving various mathematical proportions and identifying means and extremes within given equations. Explore intricate relationships between variables and learn how to manipulate equations to find unknowns effectively. Suitable for learners seeking to improve their understanding of ratios and proportions in algebra, this resource offers practical examples to solidify your comprehension of the concepts. Master these skills to excel in mathematics and application of proportional reasoning.

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Solve Proportions and Identify Means and Extremes in Mathematical Equations

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  1. Solve the proportion. 51.84 = 14.4 x x = 3.6 4.8 = x 14.4 10.8

  2. Solve the proportion. 5x = 36 x = 7.2 5 = 3 12 x

  3. Solve the proportion. 34x = 132.6 x = 3.9 x = 8.5 15.6 34

  4. Identify the means and the extremes in the proportion. Means: 14.4 & x Extremes: 4.8 & 10.8 4.8 = x 14.4 10.8

  5. x = 8.5 15.6 34 Identify the means and the extremes in the proportion. Means: 34 & x Extremes: 8.5 & 15.6

  6. 2 = x a 5b Identify the means and the extremes in the proportion. Means: a & x Extremes: 2 & 5b

  7. 2•5b = ax Which proportion is equivalent to 5b = a x 2 2 = x 5b a a = 2 5b x 2 = x a 5b 5b•2 = ax yes! 2a = 5bx no ax = 5b•2 yes!

  8. 3ez = 7x Which proportion is equivalent to 7 = e x 3z 3z = x 7 e e = 3z 7 x x = e 3z 7 3z•7 = ex nope 3ez = 7x yes ex = 3z•7 no

  9. ∆JAB ~∆RKM. Find the value of x. M J 7x – 4 3x 3 A K B R 5 6x 3 = 3x 5 7x - 4 21x – 12 = 15x 6x = 12 x = 2

  10. ∆FAT ~∆PIG. Find the value of x. T G 7 4x + 1.5 8 A P F I 4x – 1 6 28x – 7 = 24x + 9 4x = 16 x = 4 7 = 4x + 1.5 6 4x – 1

  11. ∆TEA ~∆YUM. Find the value of x. T M 3x – 5 2x – 1 8 A Y E U x + 1 12 16x – 8 = 12x + 12 4x = 20 x = 5 8 = 12 x + 1 2x – 1

  12. DFE SSS~ ∆ABC ~∆______ by _______ A D 8 30 12 20 B E C F 30 = 20 . 12 8 240 = 240 √ 30 = 27.5 . 12 11 330 = 330 √ 27.5 11

  13. AED SAS~ ∆ABC ~∆______ by _______ C D 27 8 A 9 24 E 8 = 9 . 24 27 216 = 216 √ B

  14. AED AA ∆ABC ~∆______ by _______ C D A E B

  15. ∆ABC ~∆______ by _______ A D 18 12 22 15 B E C F 15 = 12 . 22.5 18 270 = 270 √ 15 = 14 . 22.5 22 330 ≠ 315 NOT ~ 14 22.5

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