2 Warm Up Write each fraction in simplest form. 4 48 1 12 9 135 1 15 2. 1.Convert the following measurements.inches = feet16feet = inches222inches = feet27
3 CaliforniaStandardsNS Use proportions to solve problems (e.g., determine the value of N if T = , find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.4 7N 21
5 This HO gauge model train is a scale model of a historic train This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HOgauge model train is187This means that each dimension of the model is of the corresponding dimension of the actual train.187
6 A scale is the ratio between two sets of measurements A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train.A scale drawing is a proportional two-dimensional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.
7 Additional Example 1: Finding a Scale Factor Identify the scale factor.You can use the lengths or widths to find the scale factor.RoomBlueprintLength (in.)14418Width (in.)10813.5blueprint lengthroom length1814418==Write a ratio. Then simplify.blueprint widthroom width13.510818==Write a ratio. Then simplify.18The scale factor is .
8 Identify the scale factor. Check It Out! Example 1Identify the scale factor.Model AircraftBlueprintLength (in.)122Wing span (in.)183blueprint lengthaircraft length21216==Write a ratio. Then simplify.blueprint wing spanaircraft wing span31816==Write a ratio. Then simplify.The scale factor is .16
9 Additional Example 2: Using Scale Factors to Find Unknown Lengths A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches.The scale factor is . Find the size of the original photograph to the nearest tenth of an inch.51posterphoto51Think:=36l51=Write a proportion to find the length l.5l = 36Find the cross products.l = 7.2Divide.
10 Additional Example 2 Continued A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches.The scale factor is . Find the size of the photograph.51posterphoto51Think:=20.5w51Write a proportion to find the width w.=5w = 20.5Find the cross products.w = 4.1Divide.The photo is 7.2 in. long and 4.1 in. wide.
11 factor is . Find the size of the dollhouse. 1.5 1 Check It Out! Example 2Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scalefactor is Find the size of the dollhouse.1.51dollhouseblueprint1.51Think:=l45=1.51Write a proportion to find the length l.Find the cross products.l = 45 · 1.5l = 67.5Multiply.
12 Check It Out! 2 ContinuedMary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scalefactor is Find the size of the dollhouse.1.51dollhouseblueprint1.51Think:=w241.51Write a proportion to find the width w.=w = 24 · 1.5Find the cross products.w = 36Multiply.The dollhouse is 67.5 inches long and 36 inches wide.
13 Additional Example 3: Measurement Application On a road map with a scale of 1.5 inches = 60 miles, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities?Let d be the actual distance between the cities.1.5607.5d=Write a proportion.1.5 · d = 60 · 7.5Find the cross product.1.5d = 450Multiply.1.5d1.54501.5=Divide both sides by 1.5.d = 300The distance between the cities is 300 miles.
14 Check It Out! Example 3On a road map with a scale of 1 inch = 50 kilometers, the distance between Dallas and Houston is 7 inches. What is the actual distance between the two cities?Let d be the actual distance between the cities.1507d=Write a proportion.1 · d = 50 · 7Find the cross products.1d = 350Multiply.d = 350The distance between the cities is 350 kilometers.