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Introduction to Proportions & Using Cross Products Lesson 6-3 & 6-4

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CCS: 6.RP.3. Use Proportional reasoning to solve real-world and mathematical problems 6.RP.3.d Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Objectives: Students will be able to: –Test Ratios and Proportions –Complete and Identify Proportions –Use cross multiplication to solve proportions

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Vocabulary A proportion is an equation stating that two ratios are equal. To prove that two ratios form a proportion, you must prove that they are equivalent. To do this, you must demonstrate that the relationship between numerators is the same as the relationship between denominators.

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Video Explanations for Proportions Identifying Proportions

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Examples: Do the ratios form a proportion? 7 10, 21 30 x 3 Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators. 8 9, 2 3 ÷ 4 ÷ 3 No, these ratios do NOT form a proportion, because the ratios are not equal.

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Completing a Proportion Determine the relationship between two numerators or two denominators (depending on what you have). Execute that same operation to find the part you are missing.

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Example 35 40 = 7 ÷ 5 8

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Video for Examples Using Cross Products Cross Products Proportional RelationshipsCross Products Proportional Relationships Using Mental Math to Solve Proportions

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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: 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: 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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Classwork: Play Dirt Bike Proportions to practice solving proportions. You can play against up to 3 friends! Try this interactive math lesson to solve proportions. Homework Time- 6-3 & 6-4 HandoutDirt Bike Proportionsmath lesson

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