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Proportions Mrs. Hilton’s Class

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Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures. What do we mean by similar? - Similar describes things which have the same shape but are not the same size. 1 2 4 8 = 1:3 = 3:9

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We solve using Cross Products When you have a proportion (two equal ratios), then you have equivalent cross products. Find the cross product by multiplying the denominator of each ratio by the numerator of the other ratio.

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Example 1: Do the ratios form a proportion? Check using cross products. 4 12, 3 9 12 x 3 = 36 9 x 4 = 36 These two ratios DO form a proportion because their cross products are the same.

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Example 2 5 8, 2 3 8 x 2 = 16 3 x 5 = 15 No, these two ratios DO NOT form a proportion, because their cross products are different.

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Solving a Proportion Using Cross Products Use the cross products to create an equation. Solve the equation for the variable using the inverse operation.

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Example 3: Solve the Proportion k 17 = 20 68 Start with the variable. = 68k17(20) Simplify. 68k=340 Now we have an equation. To get the k by itself, divide both sides by 68. 68 k = 5

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Example 4 These two stick figures are similar. As you can see both are the same shape. However, the bigger stick figure’s dimensions are exactly twice the smaller. So the ratio of the smaller figure to the larger figure is 1:2 (said “one to two”). This can also be written as a fraction of ½. A proportion can be made relating the height and the width of the smaller figure to the larger figure: 2 feet 4 feet 8 feet 4 feet 4 ft 2 ft = 8 ft 4 ft

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Solving Proportional Problems So how do we use proportions and similar figures? Using the previous example we can show how to solve for an unknown dimension. 2 feet 4 feet 8 feet ? feet

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Solving Proportion Problems First, designate the unknown side as x. Then, set up an equation using proportions. What does the numerator represent? What does the denominator represent? Then solve for x by cross multiplying: 2 feet 4 feet 8 feet ? feet 4 ft 2 ft = 8 ft x ft 4x = 16 X = 4

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Try One Yourself Knowing these two stick figures are similar to each other, what is the ratio between the smaller figure to the larger figure? Set up a proportion. What is the width of the larger stick figure? 4 feet 8 feet 12 feet x feet

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Homework Time PINK Book Pg. 429- 430 # 1- 24 Together we will do numbers 1 and 5! Remember to show your work!!!

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