1 / 22

Example 1

Example 1. In a survey of American families, 150 families had a total of 360 children. What is the ratio of children to families? On average, how many children are there per family?. Make sure you pay attention to the order of the wording. 360/150 2.4 children/family. What is a Ratio?.

tova
Download Presentation

Example 1

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. Example 1 In a survey of American families, 150 families had a total of 360 children. What is the ratio of children to families? On average, how many children are there per family? Make sure you pay attention to the order of the wording 360/150 2.4 children/family

  2. What is a Ratio? A ratiois a comparison of two quantities, usually by division. • The ratio of a to b is a:b or • Order is important! • Part: Part • Part: Whole • Whole: Part • Units, sometimes important

  3. 6.1 Ratio and Proportion Objectives: • To recognize and use ratios and proportions to solve problems

  4. Example 2 Find the first 13 terms in the following sequence: 1, 1, 2, 3, 5, 8, … 13,21,34,55,89,144,233 This is called the Fibonacci Sequence!

  5. Foxtrot

  6. Example 3 What happens when you take the ratios of two successive Fibonacci numbers, larger over smaller? What number do you approach? ETC!

  7. The Golden Ratio What happens when you take the ratios of two successive Fibonacci numbers, larger over smaller? What number do you approach? It’s the Golden Ratio = 1.61803398…

  8. What’s a Proportion? When two ratios are equal, it’s called a proportion. • What’s an example of a proportion? What ratio is equal to ½? • Proportions are often used in solving problems involving similar objects.

  9. Solving a Proportion What’s the relationship between the cross products of a proportion? 2.4150 3601 They’re equal!

  10. Solving a Proportion Cross Products Property In a proportion, the product of the extremes equals the product of the means.

  11. Solving a Proportion To solve a proportion involving a variable, simply set the two cross products equal to each other. Then solve! 1525 275x

  12. Example 4 Solve the proportion. 50x = 1950 x=39

  13. Example 5 Solve the proportion. Show your work in your notebook. x= -6 or 1

  14. More Proportion Properties INTERESTING, huh?

  15. Exercise 1 If you work for 2 weeks and earn $380, what will you expect to earn in 15 weeks? Show your work in your notebook $2850

  16. Exercise 2 Solve for y: Show your work in your notebook y=2

  17. Exercise 3 Which is longer: a yardstick or a meter stick? (Use the conversion factor 1 in. = 2.54 cm) Remember: 1 m = 100 cm Show work in your notebook. Meter stick

  18. Exercise 4 The sides of a rose garden in the shape of a right triangle are in the ratio of 8:15:17. If the perimeter is 60 ft, what is the length of the shortest side? How are you going to do this one? 12 Think about what perimeter means Work it out in your notebook.

  19. The Greeks, Again! The Greeks used the Golden Ratio to do everything from making a pentagram, to constructing a building, to combing their hair.

  20. The Golden Rectangle If you make a rectangle with sides that have the Golden Ratio, you’ve made a sparkly Golden Rectangle.

  21. Extra Credit Opportunities • Construct a Golden Rectangle with a compass and straightedge and explain how it demonstrates the Golden Ratio

More Related