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Chapter 7 Section 1 Ratios and Proportions

Chapter 7 Section 1 Ratios and Proportions. Objectives . Students will be able to write and solve ratios Students will be able to write and solve proportions. Ratio. Comparison of two quantities by division Written as: a/ b a : b a to b Always write in simplest form (reduced form)

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Chapter 7 Section 1 Ratios and Proportions

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  1. Chapter 7 Section 1Ratios and Proportions

  2. Objectives Students will be able to write and solve ratios Students will be able to write and solve proportions

  3. Ratio • Comparison of two quantities by division • Written as: • a/b • a : b • a to b • Always write in simplest form (reduced form) • Make sure units of measure are the same

  4. Example A bonsai tree 18 in wide and stands 2 ft tall. What is the ratio of the width compared to the height? First covert measurements to either inches or feet Then write the ratio in simplest form 18 : 24  3 : 4

  5. Example A pigmy rattlesnake has average length of 18 inches, while a Western diamondback rattlesnake averages 5ft. 6in. What is the ratio of the length of a pigmy to a Western diamondback rattlesnake? 18 : 66  3 : 11

  6. Dividing Quantities into Ratios The measures of two supplementary angles are in the ratio 1:4. What are the measures of the angles? Write the ratio in words: angle 1angle 2 Then write using variables: x 4x Set up an equation: x + 4x = 180 Solve the equation: x = 36 Substitute x back into the ratioAngle 1 = 1(36) = 36 Angle 2 = 4(36) = 144

  7. Dividing Quantities into Ratios The measures of two complementary angles are in the ratio 1:3. What are the measures of the angles? Write the ratio in words: angle 1 angle 2 Then write using variables: x 3x Set up an equation: x + 3x = 90 Solve the equation: x = 22.5 Substitute x back into the ratioAngle 1 = 1(22.5) = 22.5 Angle 2 = 3(22.5) = 67.5

  8. Extended Ratio • Compares 3 or more numbers • Written as • a : b : c

  9. Example • The lengths of the sides of a triangle are in the extended ratio 4 : 7 : 9. The perimeter is 60 cm. What are the lengths of the sides? • Write an equation: 4x + 7x + 9x = 60 • Solve for x: x = 3 • So the lengths of the sides are: • 4(3) = 12 • 7(3) = 21 • 9(3) = 27

  10. Proportions When two ratios are equal Use cross products to solve proportions

  11. Properties of Proportions

  12. Solving 9 = a2 14 15 = 3m+1 m

  13. Writing Equivalent Proportions • x/6 = y/7 What ratio completes the equivalent proportion? • x/y = ? • 6/x = ? • (y + 7)/7 = ?

  14. Homework Pg. 436 #9 – 32, 40 – 43

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