1 / 14

Warm Up Solve each proportion.

3 5. x 75. 6 x. 2.4 8. =. =. 9 27. x 6. =. Warm Up Solve each proportion. 1. 2. x = 45. x = 20. x 3.5. 8 7. 3. 4. x = 4. =. x = 2. Vocabulary. Scale Scale drawing Scale model Scale factor Indirect Measurement.

stuart-smith
Download Presentation

Warm Up Solve each 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. 3 5 x 75 6 x 2.4 8 = = 927 x 6 = Warm Up Solve each proportion. 1. 2. x = 45 x = 20 x 3.5 8 7 3. 4. x = 4 = x = 2

  2. Vocabulary • Scale • Scale drawing Scale model Scale factor Indirect Measurement

  3. A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units. A scale drawing is a two-dimensional drawing of an object that is proportional to the object. A scale model is a three-dimensional model that is proportional to the object.

  4. Write a proportion using the scale. Let x be the actual length of the amoeba. 1000 8 mm = 1 x mm Class Example Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? 1000 x = 1 8 The cross products are equal. Solve the proportion. x = 0.008 The actual length of the amoeba is eight thousandths of a millimeter.

  5. Write a proportion using the scale. Let x be the actual length of the fiber. 10,000 1 mm = 1 x mm Partner Practice Under a 10,000:1 microscope view, a fiber appears to have length of 1 mm. What is its actual length? 10,000 x = 1 1 The cross products are equal. x = 0.0001 Solve the proportion. The actual length of the fiber is 1 ten-thousandths of a millimeter.

  6. Reading Math The scale a:b is read “a to b.” For example, the scale 1 cm:4 m is read “one centimeter to four meters.” Scale factor is the ratio of a length on a scale drawing or model to the corresponding length on the actual object. When finding a scale factor, you must use the same measurement units. You can use a scale factor to find unknown dimensions.

  7. 1 cm 4 cm scale length . Set up proportion using x m 12 m actual length Class Practice The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale? = 1  12 = x4 Find the cross products. 12 = 4x 3 = x Divide both sides by 4. The scale is 1 cm:3 m.

  8. 2 in. 2 in. 1 in. 1 = = 3 ft 36in. 18 in. 18 1 The scale factor for the model is . Now set up a proportion. 18 1 h in. = 18 324 in. Partner Practice A model of a 27 ft tall house was made using a scale of 2 in.:3 ft. What is the height of the model? Find the scale factor. = Convert to same measurements Let h equal the height of the model. What is “h”??? Convert: 27 ft = 324 in. 324 = 18h Find the cross products. 18 = h Divide both sides by 18. The height of the model is 18 in.

  9. 5 cm 50 mm = = 500,000,000 0.0000001 mm 0.0000001 mm Individual Practice A DNA model was built using the scale 5 cm: 0.0000001 mm. If the model of the DNA chain is 20 cm long, what is the length of the actual chain? Find the scale factor. The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain.

  10. 500,000,000 20 cm 1 x cm Individual Practice...continued = Set up a proportion. 500,000,000x = 1(20) Find the cross products. Divide both sides by 500,000,000. x = 0.00000004 The length of the DNA chain is 4  10-8 cm.

  11. How is scale different than rate? • Discuss with your partner • Write an answer (in words)

  12. Sometimes, distances cannot be measured directly. One way to find such a distance is to use indirect measurement, a way of using similar figures and proportions to find a measure.

  13. AB EF B AC EG 3 ft 3 9 A C 4 x 4 ft F 3x 36 9 ft 3 3 G x E Class Practice Triangles ABC and EFG are similar. Find the length of side EG. Set up a proportion. = Substitute 3 for AB, 4 for AC, 9 for EF, and x for EG. = 3x = 36 Find the cross products. Divide both sides by 3. = Divide both sides by 3. x = 12 The length of side EG is 12 ft.

  14. E DE GH 7 in EF HI 2 8 7 x D F H x 2x 56 8 in 2 2 I G Individual Practice Triangles DEF and GHI are similar. Find the length of side HI. = Set up a proportion. 2 in Substitute values for DE, EF, GH, and HI. = 2x = 56 Find the cross products and solve for x. = x = 28 The length of side HI is 28 in.

More Related