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Bell Ringer

Bell Ringer. Ratios and Proportions . A ratio is a comparison of a number “a” and a nonzero number “b” using division . Example 1. Simplify Ratios. Simplify the ratio. 60 cm : 200 cm. a. b. SOLUTION. a. 60 cm : 200 cm can be written as the fraction . 3. 60 ÷ 20.

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Bell Ringer

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  1. Bell Ringer

  2. Ratios and Proportions • A ratio is a comparison of a number “a” and a nonzero number “b” using division

  3. Example 1 Simplify Ratios Simplify the ratio. 60 cm : 200 cm a. b. SOLUTION a. 60 cm : 200 cm can be written as the fraction . 3 60 ÷ 20 Divide numerator and denominator by their greatest common factor, 20. = 10 200 ÷ 20 60 cm 60 cm 3 ft 200 cm 18 in. 200 cm 3 is read as “3 to 10.” Simplify. = 10

  4. Example 1 Multiply. Divide numerator and denominator by their greatest common factor, 18. Simplify Ratios b. = Substitute 12 in. for 1 ft. = = = 3 ·12 in. 3 ft 36 ÷ 18 2 36 in. 18 in. 18 ÷ 18 1 18 in. 18 in. 2 Simplify. is read as “2 to 1.” 1

  5. Example 2 Use Ratios In the diagram, AB : BC is 4 : 1and AC = 30. Find AB and BC. SOLUTION Let x = BC. Because the ratio of AB to BC is 4 to 1, you know that AB = 4x. Segment Addition Postulate AB + BC= AC Substitute 4xfor AB,x for BC, and 30 for AC. 4x + x = 30 Add like terms. 5x = 30 Divide each side by 5. x = 6

  6. Example 2 Use Ratios To find AB and BC, substitute 6 for x. AB = 4x = 4 ·6 = 24 BC = x = 6 So, AB = 24 and BC = 6. ANSWER

  7. Example 3 Use Ratios The perimeter of a rectangle is 80 feet. The ratio of the length to the width is 7 : 3. Find the length and the width of the rectangle. SOLUTION The ratio of length to width is 7 to 3. You can let the length l = 7x and the width w = 3x. Formula for the perimeter of a rectangle 2l + 2w= P 2(7x) + 2(3x) = 80 Substitute 7x for l, 3x for w, and 80 for P. Multiply. 14x + 6x = 80 20x = 80 Add like terms. Divide each side by 20. x = 4

  8. Example 3 Use Ratios To find the length and width of the rectangle, substitute 4 for x. l = 7x = 7 ·4 = 28 w = 3x = 3 ·4 = 12 The length is 28 feet, and the width is 12 feet. ANSWER

  9. Now You Try  1. In the diagram, EF : FG is 2 : 1 and EG = 24. Find EF and FG. 2. The perimeter of a rectangle is 84 feet. The ratio of the length to the width is 4 : 3. Find the length and the width of the rectangle. EF = 16;FG = 8 length, 24 ft; width, 18 ft ANSWER ANSWER

  10. An equation that states that two ratios are equal is called a proportion

  11. Example 4 Solve a Proportion Solve the proportion . = SOLUTION = Write original proportion. 5·6=3(y + 2) Cross product property 30 = 3y + 6 Multiply and use distributive property. y + 2 y + 2 30 – 6 = 3y + 6 – 6 Subtract 6 from each side. 6 6 5 5 24 = 3y Simplify. 3 3 3y 24 = Divide each side by 3. 3 3 8 = y Simplify.

  12. = 4. 5. = Now You Try  Solve the proportion. 3 6 = 4 3. ANSWER x 8 5 15 9 ANSWER y 3 14 10 m + 2 5 ANSWER 5

  13. Complete #s 2-44 even only

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