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8-2 6th grade math Proportions

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**Objective To solve proportions using equivalent ratios.**

Why? To use ratios to compare two quantities when enlarging (increasing) or reducing (decreasing) ratios. To solve for missing sides of geometric shapes. To solve for ‘x’ in ratios or proportions.

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**California State Standards**

NS 1.3 : Use proportions to solve problems (e.g., determine the value of N if 4/7 = n/21) NS 1.0 : Solve problems involving … proportions … MR 1.1: Analyze problems by identifying relationships, …

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**Vocabulary Proportion**

An equation stating that two ratios are equivalent 35 = 105 = 16

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**How to Know if 2 Ratios are Proportional**

1) Solve as stated in the previous lesson. Cross multiply the numbers. 2) Write the numbers from cross multiplying. 3) Compare the ‘numbers.’ If they are the same, then the ratios are proportional. If they are not, the ratios are not proportional. 3 ? x 30 = 90 5 x 18 = 90 3 = 18

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**How to Solve Proportions- Solving for ‘x’**

As in the previous lesson, Cross multiply Divide by the last number Check for reasonableness. 15 = n x 7 = = 3

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**Another Way to Solve Proportions- Solving for ‘x’**

18 = 9 x 18 ÷ 2 = 9 → 12 ÷ 2 = 6 → or 9 x 2 = 18 ← 12 ÷ 2 = 6 → 6 1) Re-write as equivalent fractions, if possible. Decide how the known portions- the numerators or denominators- were able to change ‘into’ each other. Did it get multiplied or divided by a special number? Pay attention to the order. 2) If traveling in the same motion, multiply or divide the other portion by the same number. 3) If traveling in the opposite motion, use inverse operations. 3) Check the results for reasonableness.

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**Try It! 60 60 4 12 yes (or x 3) 5 15 63 72 Are these equivalent?**

yes (or x 3) 2) 3 , no < 3) 2 , yes (or x 9) 4) 5 , yes (or x8) Try It! Are these equivalent? 4 , 12 2) 3 , 9 3) 2 , 18 4) 5 , 40

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**Objective Review To solve proportions using equivalent ratios.**

Why? You can now use ratios to compare two quantities when enlarging (increasing) or reducing (decreasing) ratios. You can solve for missing sides of geometric shapes. You can solve proportions by finding equivalent ratios. You can solve for x in a proportion or ratio problem.

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**Independent Practice Complete problems 6-15**

10-13 = solving for x Copy original problem first. Show all work! If time, complete Mixed Review: 16-22 If still more time, work on Accelerated Math.

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