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Lesson 3.6: Ratios and Proportions A ratio is a comparison of two numbers by division. The ratio of x to y can be expressed the following ways-> x to y 𝑥 𝑦 x:y An equation stating that two ratios are equal is called a proportion. Determine Whether Ratios Form a Proportion 7 49 𝑎𝑛𝑑 56 8 Method 1: Reduce both fractions Method 2: Use cross products means-extremes property In any proportion, the product of the means equals the product of the extremes. Some people learn this as "cross products are equal in any proportion." means In the proportion a/b = c/d, the numbers b and c. extremes In the proportion a/b= c/d, the numbers a and d. Further Examples: Determine whether each pair of ratios forms a proportion: .25 1.25 , 2 .6 4 16 , 5 20 Solving Proportions 𝑛 3 = 12 8 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 turn the pedals during the trip? In a road atlas, the scale for the map of Connecticut is 5 inches = 41 miles. The scale for the map of Texas is 5 inches = 44 miles. What are the distances represented by 2 ½ inches on each map? Homework: pages 158-15912-34 EVEN