1 / 15

Ratio and Proportion

Ratio and Proportion. 7-1. 5 ft. 5 ft. 5 ft. 20 in . 20 in . 20 in . b. . a. . 64 m : 6 m. 64 m. 64 m. Write. 64 m : 6 m as. . 6 m. 6 m. a. . 3. 32. 1. 3. =. =. 32 : 3. To simplify a ratio with unlike units, multiply by a conversion factor. b.

overton
Télécharger la présentation

Ratio and Proportion

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. Ratio and Proportion 7-1

  2. 5 ft 5 ft 5 ft 20 in. 20 in. 20 in. b. a. 64 m : 6 m 64 m 64 m Write 64 m : 6 mas . 6 m 6 m a. 3 32 1 3 = = 32 : 3 To simplify a ratio with unlike units, multiply by a conversion factor. b. 60 12 in. 20 1 ft = = = EXAMPLE 1 Simplify ratios Simplify the ratio. SOLUTION Then divide out the units and simplify.

  3. 24 24 3 3 Write 24 yards : 3 yards as 8 1 = = 8 : 1 for Example 1 GUIDED PRACTICE Simplify the ratio. 1. 24 yardsto 3 yards SOLUTION Then divide out the units and simplify.

  4. 150 6 1 4 150cm 1m = = 6m 100cm for Example 1 GUIDED PRACTICE Simplify the ratio. 2. 150 cm : 6 m SOLUTION To simplify a ratio with unlike units, multiply by a conversion factors. = 1 : 4

  5. x 5 x 5 a. = 16 10 16 10 Solve the proportion. ALGEBRA a. = 5 16 = 80 10 x = 10 x 8 x = EXAMPLE 4 Solve proportions SOLUTION Write original proportion. Cross Products Property Multiply. Divide each side by 10.

  6. 1 1 2 2 b. = y + 1 y + 1 3y 3y b. = 1 3y 2 (y + 1) = 3y 2y + 2 = y 2 = EXAMPLE 4 Solve proportions SOLUTION Write original proportion. Cross Products Property Distributive Property Subtract 2y from each side.

  7. 2 2 5 5 5. = x 8 8 x = 2 8 5 x = 16 5 x = 16 x = 5 for Example 4 GUIDED PRACTICE SOLUTION Write original proportion. Cross Products Property Multiply. Divide each side by 5 .

  8. 1 1 4 4 6. = x – 3 3x x – 3 3x = 3x = 4(x – 3) 3x = 4x – 12 3x – 4x = – 12 – x x – 12 12 = = for Example 4 GUIDED PRACTICE SOLUTION Write original proportion. Cross Products Property Multiply. Subtract 4x from each side.

  9. y – 3 y y 7. = = 7 14 14 y – 3 7 = 7 y 14(y – 3) 14y – 42 = 7y 14y –7y = 42 y 6 = for Example 4 GUIDED PRACTICE SOLUTION Write original proportion. Cross Products Property Multiply. Subtract 7y from each side and add 42 to each side. Subtract , then divide

  10. Painting You are planning to paint a mural on a rectangular wall. You know that the perimeter of the wall is 484feet and that the ratio of its length to its width is 9 : 2. Find the area of the wall. STEP 1 Write expressions for the length and width. Because the ratio of length to width is 9 : 2, you can represent the length by 9xand the width by 2x. EXAMPLE 2 Use a ratio to find a dimension SOLUTION

  11. STEP 2 Solve an equation to findx. 2l + 2w = P 484 2(9x) + 2(2x) = 484 22x = x 22 = Evaluate the expressions for the length and width. Substitute the value of xinto each expression. STEP 3 The wall is 198feet long and 44feet wide, so its area is 198 ft 44 ft = 8712 ft. 2 EXAMPLE 2 Use a ratio to find a dimension Formula for perimeter of rectangle Substitute for l, w, and P. Multiply and combine like terms. Divide each side by 22. Length= 9x = 9(22) = 198 Width = 2x = 2(22) = 44

  12. ALGEBRA The measures of the angles in CDE are in the extended ratio of 1 : 2 : 3. Find the measures of the angles. o o o o 180 x + 2x + 3x = 6x 180 = x = 30 ANSWER o o o o o The angle measures are 30 , 2(30 ) = 60 , and 3(30 ) = 90. EXAMPLE 3 Use extended ratios SOLUTION Begin by sketching the triangle. Then use the extended ratio of 1 : 2 : 3 to label the measures as x° , 2x° , and 3x° . Triangle Sum Theorem Combine liketerms. Divide each side by 6.

  13. STEP 1 Write expressions for the length and width. Because the ratio of length is 7 : 5, you can represent the length by 7xand the width by 5x. for Examples 2 and 3 GUIDED PRACTICE 3. The perimeter of a room is 48 feet and the ratio of its length to its width is 7 : 5. Find the length and width of the room. SOLUTION

  14. STEP 2 Solve an equation to findx. 2l + 2w = P 48 2(7x) + 2(5x) = 48 24x = x 2 = Evaluate the expressions for the length and width. Substitute the value of xinto each expression. STEP 3 for Examples 2 and 3 GUIDED PRACTICE Formula for perimeter of rectangle Substitute for l, w, and P. Multiply and combine like terms. Length= 7x + 7(2) = 14 ft Width = 5x + 5(2) = 10 ft

  15. 4.A triangle’s angle measures are in the extended ratio of 1 : 3 : 5. Find the measures of the angles. x 3x 5x o o o o 180 x + 3x + 5x = 9x 180 = x = 20 ANSWER o o o o o The angle measures are 20 , 3(20 ) = 60 , and 5(20 ) = 100. for Examples 2 and 3 GUIDED PRACTICE SOLUTION Begin by sketching the triangle. Then use the extended ratio of 1 : 3 : 5 to label the measures as x° , 2x° , and 3x° . Triangle Sum Theorem Combine liketerms. Divide each side by 9.

More Related