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NOTES 3-6 Ratios and Proportions Pages 155-157 I can determine whether two ratios form a proportion and I can solve for an unknown using proportions. Main Idea Ratio Details A comparison of two numbers by division. x x to y x:y y An equation stating that two ratios are equal. Proportion Determining if two ratios form a proportion 4 6 is a proportion. 2 3 Method 1: If both the numerator and denominator of one ratio can be multiplied or divided by the same number to obtain the second ratio, then the ratios form a proportion. See Example 1 on page 155 Method 2: If the cross products (numerator of one ratio multiplied by the denominator of the other ratio) are equal, then the ratios form a proportion. See Example 2 on page 156 In the proportion a c b d Extremes of a proportion a and d are the extremes. In the proportion Means of a proportion a c b d b and c are the extremes. In a proportion, the product of the extremes is equal to the product of the means. Means-Extremes Property of Proportion If a c , then ad = bc. b d 4 6 Since , 4(3) = 6(2) or 12 = 12. 2 3 Rate A ratio of two measurements having different units of measure. Scale A ratio or rate that is used in the making of a model or drawing of something that is too large or too small to be conveniently drawn at actual size. Example 1: Determine whether the ratios 7 49 and form a proportion. 8 56 0.25 1.25 , 0.6 2 Example 2: Use cross products to determine whether each pair of ratios form a proportion. 4 16 , 5 20 Example 3: Solve the proportion n 3 12 8 Example 4: The gear on a bicycle is 8:5. This means that for every 8 turns of the pedals, the wheels turn 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? Example 5: 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 = 144 miles. What are the distances in miles represented by 2 12 inches on each map? Homework: Workbook Page 22 #3-33 multiples of 3 and #34, 35