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A ratio is a comparison of two quantities by division. The ratio of 1 teacher to 24 students can be written as: In Algebra, we prefer to write ratios as fractions. A statement that two ratios are equivalent, such as is called a proportion. 24 1 2 4 3 6 Click OK or 1:24 = Cross products, or cross multiplication can be used to solve for a missing value in a proportion. Find cross products Use inverse operations to solve for x Simplify Find the value of x. (30)(x) 30x 30 30 2 x 30 675 x = 45 Click OK = = = (675)(2) 1350 Use cross products to solve the proportions for x. 5x = x = 3 x 5 100 = Type in your answers 20x = x 7.5 8 20 x = = If you got x=60 and x=3, then you were correct. Solving proportions using cross products is a fairly easy process. The difficulty arises during the application with similar shapes. Similar (~) shapes have exactly the same shape, but not necessarily the same size. The corresponding sides of similar shapes are proportional. Being able to identify the corresponding sides will play a vital role in the set up of a proportion. Click OK Color coding and placing the shapes in the same relative position is extremely useful. Type your answers in alphabetical order. C A B ∆ABC ~ ∆DEF Can you pair the corresponding side of the given triangles? AC corresponds to BC corresponds to AB corresponds to F E D Now let's use similar shapes and proportions to find the length of a missing side. C x ft 12 ft A B ∆ABC ~ ∆DEF x ft 8 ft 5 5x = 96 5 5 x x = 19.2 ft = = ( ) 12 ft 5 ft 8 ( ) 12 F 8 ft 5 ft E D Click OK Now let's use similar shapes and proportions to find the length of a missing side. B A x ft C 6 ft D ABCD ~ EFGH x ft ft Type in your answers x = = number E F ft ft 2 ft units G 4 ft H Now lets look at using proportions in a different way: ??? A building has a shadow that is 25 feet long. A person 6 feet tall cast a shadow that is 1 foot long. How tall is the building? 25 ft Type in your answers 6 ft The building is ft tall. 1 ft Begin by setting up your proportion. Then solve it using cross products. 6 ft A 6 ft tall tent standing next to a cardboard box casts a 9 ft shadow. If the cardboard box casts a shadow that is 6 ft long then how tall is it? Finally, try the last two problems on your own: If you answered 150 ft - Congratulations! 9ft ??? Type in your answer 6 ft Begin by setting up your proportion. Then solve it using cross products. The box is ft tall A statue that is 12 ft tall cast a shadow that is 15 ft long. Find the length of the shadow that an 8 ft cardboard box casts. The shadow if the cardboard box is ft long. Begin by drawing a picture that represents the problem. Then set up your proportion and solve it using cross products. Type in your answer |