1. 6.1 – Ratios, Proportions, and the Geometric Mean

2. Ratio: The relationship between 2 numbers, has no units a:b abab a to b Always simplify them!!!

3. 1. Find the ratio of the width to the length of the rectangle. Then simplify the ratio.

6. 2. Use the number line to find the ratio of the distances.

10. Proportion: To solve: An equation that states two ratios are equal Cross multiply! ad = bc

11. 3. Solve the proportion. 4x4x= 36 4 x = 9 13

12. y= 9 y = 9 3. Solve the proportion.

13. 4(x + 2)= 20 x = 3 4x + 8 = 20 4x = 12 x = 3 12 1 5 x + 2 = 5 3. Solve the proportion.

14. 3(x + 8)= 6x6x 8 = x 3x + 24 = 6x 24 = 3x x = 8 12 2x = x + 8 3. Solve the proportion.

15. 24(x – 12)= 8x8x 18 = x 24x – 288 = 8x –288 = –16x x = 18 3 1 3x – 36 = x 2x – 36 = 0 2x = 36 3. Solve the proportion.

16. 4(y + 1)= 2(y + 4) y = 2 4y + 4 = 2y + 8 2y = 4 2y + 4 = 8 1 2 y = 2 y + 2 = 4 2y + 2 = y + 4 3. Solve the proportion.

17. 4. The ratio of two side lengths for the triangle is given. Solve for the variable. AC:AB is 2:3. 3x3x= 24 3 x = 8 14

18. AB:CB is 2:1. 16x= 48 16 x = 3 18 3 1 4. The ratio of two side lengths for the triangle is given. Solve for the variable.

19. AC:BC is 7:4. 7(2x + 4)= 84 x = 4 14x + 28 = 84 14x = 56 13 x = 4 2x + 4 = 12 2x = 8 4. The ratio of two side lengths for the triangle is given. Solve for the variable.

20. 5. Use the given information and the diagram to find the unknown length. 3x = 2 x = 2323

21. 5. Use the given information and the diagram to find the unknown length. 3x = 24 x = 8

22. 5. Use the given information and the diagram to find the unknown length. 18x = 180 x = 10

23. 5. Use the given information and the diagram to find the unknown length. 12x = 144 x = 12

24. Geometric Mean: The square root of the product of two numbers x 2 = ab

25. 6. Find the geometric mean. 1 and 4

26. 6. Find the geometric mean. 2 and 50

27. 6. Find the geometric mean. 3 and 15

28. 6. Find the geometric mean. 7 and 14

29. HW Problem SectionPage #Assignment Spiral 6.1 6.2 360-362 367-369 11-17 odd, 23-35 odd, 39-43 odd, 49, 51 11, 12, 16, 17, 28, 29 1, 2 6.2 #28 1 12 12x = 21 x = 1.75ft