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Mastering Ratios and Proportions: A Comprehensive Lesson

This lesson focuses on understanding ratios and proportions, emphasizing their properties and applications. Students will learn how to express ratios in different ways, such as using fractions and writing them in comparative forms. Key concepts include the ratio of different groups (e.g., females to males) and recognizing when a ratio cannot be simplified. Various mathematical problems involving angles and costs will be solved to reinforce these concepts. The assignment for practice is provided, targeting odds only.

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Mastering Ratios and Proportions: A Comprehensive Lesson

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  1. I can write ratios • I can use properties of proportions Lesson 6-1

  2. Alice

  3. quotient a : b with the same units Write with : or as a fraction, a/b

  4. females : males

  5. elective : non-elective 2 : 3

  6. a : b : c Ex: ratio of freshmen to sophomores to juniors Cannot be written as a fraction

  7. 7 84 x 240 5x + 7x + 8x = 5 x 20x = 240 60 96 8 x x = 12

  8. 24° 2 x 2x + 10x + 3x = 180 3 x 15x = 180 x 10 36° 120° x = 12

  9. 7x L W 3x 3x 140 20x = x = 7 7x L = 49

  10. fractions equal diagonals

  11. 72 8y = 163.8 6x = y = 9 x = 27.3

  12. 4(2x + 3) = 40 4(x + 1) 3(x – 1) = 8x + 12 = 40 4x + 4 3x – 3 = x = -7 x = 3.5

  13. CD’s cost 3x = 3 2 89.7 = 44.85 x x = 29.9 $29.90

  14. length width 40x = 40 16 144 = 9 x x = 3.6 3.6 inches

  15. miles inches 4 x x = 14 = 1 3.5 14 miles

  16. gal miles 5 x x = 14.58333 = 120 350 14.6 gallons

  17. ? 5 wide 3.5 18 tall 5 x = 3.5 18 x = 25.7143 25.7 inches

  18. 3 : 1 : 2 oats W : R : O wheat 120 2 = x 3 x = 180

  19. ASSIGNMENT: 6-1 worksheet, do odds only

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