2Warm 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
3CaliforniaStandardsNS 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
5This 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
6A 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.
7Additional 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 .
8Identify 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
9Additional 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.
10Additional 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.
11factor 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.
12Check 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.
13Additional 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.
14Check 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.