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Section 2-6 Ratios and Proportions Date: ____________________ Homework assignment: __________________________________________ A _____________ is a comparison of two numbers by division. They can be expressed in the following ways: The ratio of two measurements having different units of measure is called a ___________. A ________ that tells how many of one item is being compared to 1 of another item is called a ____________ ________. Example: If cheese costs $2.54 for 8 slices, how much does one slice cost? Example: You are shopping for t-shirts. Which store offers the best deal? Store A: $25 for 2 shirts Store B: $45 for 4 shirts Store C: $30 for 3 shirts An equation stating that two ratios are equal is called a _____________________. Determine Whether Ratios Are Equivalent: 1. 6 2 , 10 5 2. 1 5 , 6 30 3. 10 5 , 42 21 There are names for terms in a proportion. In the example below, 4 and 10 are called the ___________________________, and 5 and 8 are called the _______________________ of the proportion. 4:5 = 8 : 10 Means-Extremes Property of Proportion: In a proportion, the _________________ of the extremes is equal to the ________________ of the means. Basically, the above property allows us to use _______________________________ to determine if two ratios form a proportion. Cross-Products: Use cross-products to determine whether each pair of ratios forms a proportion. 15 35 , 1. 36 42 2. 7 42 , 3. 8 48 3 , 9 7 14 You can find the missing value in a proportion two ways: o Using the Property of Equality (What we did in Section 2-2) o Using Solve the Following Proportions: 𝑥 = 8 1. 25 40 2. 𝑥+4 5 = 3 8 3. 9𝑥−3 9 = 5𝑥+5 3 Setting up a Proportion: The gear on a bicycle is 8:5. This means that for every 8 turns of the pedals, the wheel turns 5 times. Suppose the bicycle wheel turns about 2435 times during a trip. How many times would you have to crank the pedals during the trip? A rate called a ______________ is used to make a ____________ _______________ of something too large or too small to be convenient at actual size. Example: On a model airplane, the scale is 5 centimeters = 2 meters. If the model’s wingspan is 28.5 centimeters, what is the actual wingspan?