1 / 14

Ratios and Proportions

Simplify each ratio. 1. 2. 3. 4. 5. 20:30 6. 8 to 2 7. 2 to 8 8. 12 : 9 9. Draw a triangle. Then draw its three midsegments to form a smaller triangle. How do the lengths of the sides of the smaller triangle compare to the lengths of the sides of the larger triangle?. 2 4. 8

dafydd
Download Presentation

Ratios and Proportions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Simplify each ratio. 1. 2. 3. 4. 5. 20:30 6. 8 to 2 7. 2 to 8 8. 12 : 9 9. Draw a triangle. Then draw its three midsegments to form a smaller triangle. How do the lengths of the sides of the smaller triangle compare to the lengths of the sides of the larger triangle? 24 8 12 6 8 10 10 Ratios and Proportions Lesson 7-1 Check Skills You’ll Need (For help, go to the Skills Handbook, page 756 and Lesson 5-1.) Check Skills You’ll Need 7-1

  2. 2 ÷ 24 ÷ 2 12 8 ÷ 412 ÷ 4 23 6 ÷ 28 ÷ 2 34 10 ÷ 1010 ÷ 10 2030 20 ÷ 1030 ÷ 10 23 82 8 ÷ 22 ÷ 2 41 Ratios and Proportions Lesson 7-1 Check Skills You’ll Need Solutions 1. Divide the numerator and denominator by 2. = 2. Divide the numerator and denominator by 4. = 3. Divide the numerator and denominator by 2. = 4. Divide the numerator and denominator by 10. = 1 5. Rewrite 20:30 as . Divide the numerator and denominator by 10. = 6. Rewrite 8 to 2 as . Divide the numerator and denominator by 2. = or 4 to 1. 7-1

  3. 7. Rewrite 2 to 8 as . Divide the numerator and denominator by 2. = or 1 to 4. 8. Rewrite 12 : 9 as . Divide the numerator and denominator by 3. = or 4 : 3. 9. The lengths of the sides of the smaller triangle are the lengths of the sides of the larger triangle. 28 2 ÷ 28 ÷ 2 14 129 12 ÷ 39 ÷ 3 43 12 Ratios and Proportions Lesson 7-1 Check Skills You’ll Need Solutions (continued) 7-1

  4. Ratios and Proportions Lesson 7-1 Notes A ratiois a comparison of two quantities. You can write the ratio of a to b or a:b as the quotient when b≠0. 7-1

  5. Ratios and Proportions Lesson 7-1 Notes A proportionis a statement that two ratios are equal. 7-1

  6. Ratios and Proportions Lesson 7-1 Notes When three or more ratios are equal, you can write an extended proportion. 7-1

  7. Ratios and Proportions Lesson 7-1 Notes 7-1

  8. Ratios and Proportions Lesson 7-1 Notes Multiplying both sides ofby bdresults in the first property, called the Cross Product Property. You may state this property as “The product of the extremes is equal to the product of the means.” 7-1

  9. Ratios and Proportions Lesson 7-1 Notes In a scale drawing, the scale compares each length in the drawing to the actual length. The lengths used in a scale can be in different units. A scale might be written as 1 in. to 100 mi., 1 in. = 12 ft., or 1mm:1m. 7-1

  10. length of model length of car 4 in. 15 ft. 4 in. 180 in. 4 180 1 45 = = = = Ratios and Proportions Lesson 7-1 Additional Examples Real-World Connection A scale model of a car is 4 in. long. The actual car is 15 ft long. What is the ratio of the length of the model to the length of the car? Write both measurements in the same units. 15 ft = 15 X 12 in. = 180 in. The ratio of the length of the scale model to the length of the car is 1 : 45. Quick Check 7-1

  11. a 4 12 b b 12 ? ? Complete: If = , then = . a 4 12 b Multiply each side by 4b. 4b=   4b Cross-Product Property ab = 48 ab 12a 48 12a Divide each side by 12a. = b 12 4 a Simplify. = Ratios and Proportions Lesson 7-1 Additional Examples Properties of Proportions Quick Check 7-1

  12. 2 5 n 35 x + 1 3 x 2 a. b. = = 5n = 2(35) Cross-Product Property 3x = 2(x + 1) Cross-Product Property 5n = 70 Simplify. 3x = 2x + 2 Use the Distributive Property. n = 14 Divide each side by 5. x = 2 Subtract 2x from each side. Ratios and Proportions Lesson 7-1 Additional Examples Solving for a Variable Solve each proportion. Quick Check 7-1

  13. Let d represent the actual distance. Map distance (in.) actual distance (mi.) = 1 in. 50 mi. 1 2 3 d 1 50 Substitute. d = 50(3 ) = 1 2 Use the Cross-Product Property. d = 175 Simplify. Ratios and Proportions Lesson 7-1 Additional Examples Real-World Connection 1 2 Two cities are 3 in. apart on a map with the scale 1 in. = 50 mi. Find the actual distance. The cities are actually 175 mi. apart. Quick Check 7-1

  14. 1. A scale model of a boat is 9 in. long. The boat’s actual length is 60 ft. Find the ratio of the length of the scale model to the length of the boat. 2. Solve the proportion = . 3. A map uses the scale 1 cm = 20 mi. A county is 90 mi wide. How wide is the county on the map? If = , complete each of the following. 4. = 5. 7y = ? 6. = 10 8 15 x 1 2 4 cm x y 7 11 y x ? ? x + y y ? 11 Ratios and Proportions Lesson 7-1 Lesson Quiz 1 : 80 12 11 7 11x 18 7-1

More Related