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Week 17, Day Four HW # 61 - Begin the Group Exam (Put this on a new TOC) Warm up Evaluate the following for x = 16. 1. 3x 48 2. x 3 4 12 Evaluate the following for x = 2 . 5 1 1 3. 10x 4. x 4 10 4 Place your EXTRA CREDIT and your warm up page in the center of your table. Place your OLD HW TOC in the center of the table. Warm Up Response 24 Homework Check Practice 5-6 Check your answers ONLINE Proportions Practice- see hard copy (use document camera) • Area Volume Ratios worksheet • (we will work on this next week) Vocabulary scale drawing scale model scale scale factor 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. 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. Additional Example 1: Finding Actual Measurements Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? 1000 = 8 mm 1 x mm 1000 x = 1 8 x = 0.008 Write a proportion using the scale. Let x be the actual length of the amoeba. The cross products are equal. Solve the proportion. The actual length of the amoeba is 0.008 mm. Check It Out! Example 1 Under a 10,000:1 microscope view, a fiber appears to have length of 1 mm. What is its actual length? 10,000 = 1 mm 1 x mm 10,000 x = 1 1 x = 0.0001 Write a proportion using the scale. Let x be the actual length of the fiber. The cross products are equal. Solve the proportion. The actual length of the fiber is 0.0001 mm. Additional Example 2: Using Proportions to Find Unknown Scales A. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale? 1 cm = 2 cm xm 8m Set up proportion using 1 8 = x 2 8 = 2x Find the cross products. 4=x Divide both sides by 2. The scale is 1 cm:4 m. scale length . actual length 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.” Check It Out! Example 2 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 cm = 4 cm xm 12 m 1 12 = x 4 12 = 4x 3=x Set up proportion using Find the cross products. Divide both sides by 4. The scale is 1 cm:3 m. scale length . actual length The ratio of a length on a scale drawing or model to the corresponding length on the actual object is called the scale factor. When finding a scale factor, you must use the same measurement units. You can use a scale factor to find unknown dimensions. Additional Example 3: Using Scale Factors to Find Unknown Dimensions 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? 2 in. = 2 in. = 1 in. = 1 3 ft 36 in. 18 in. 18 The scale factor for the model is 1 = h in. 18 324 in. Find the scale factor. 1 . Now set 18 up a proportion. 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. Check It Out! Example 3 A model of a 24 ft tall bridge was made using a scale of 4 in.:2 ft. What is the height of the model? 4 in. = 4 in. = 1 in. = 1 Find the scale factor. 2 ft 24 in. 6 in. 6 1 up a proportion. The scale factor for the model is . Now set 6 1 h in. = 6 288 in. 288 = 6h 48 = h Convert: 24 ft = 288 in. Find the cross products. Divide both sides by 6. The height of the model is 48 in. Additional Example 4: Life Science Application 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. 5 cm 0.0000001 mm 50 mm = 0.0000001 mm = 500,000,000 The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain. Additional Example 4 Continued 500,000,000 1 cm = 20 x cm 500,000,000x = 1(20) x = 0.00000004 Set up a proportion. Find the cross products. Divide both sides by 500,000,000. The length of the DNA chain is 4 10-8 cm. Check It Out! Example 4 A model was built using the scale 2 cm:0.01 mm. If the model is 30 cm long, what is the length of the actual object? Find the scale factor. 2 cm 0.01 mm = 20 mm 0.01 mm = 2,000 The scale factor for the model is 2,000. This means the actual object is two thousand times larger than the model. Check It Out! Example 4 Continued 2,000 1 = 30 cm x cm 2,000x = 1(30) x = 0.015 Set up a proportion. Find the cross products. Divide both sides by 2,000. The length of the actual object is 1.5 10-2 cm. Lesson Quiz 1 1. Using a 4 in. = 1 ft scale, how long would a drawing of a 22 ft car be? 5.5 in. 2. What is the scale of a drawing in which a 9 ft wall is 6 cm long? 1 cm = 1.5 ft 3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person? 72 in.