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Ratios and Proportions Name_____________________________ Ratio - Comparison of two quantities by division. a b a:b a to b (where b ≠ 0) Usually a and b are in the same units and in simplest form. Extended ratio – Compares 3 or more numbers. a:b:c Proportion – An equation that states two ratios are equivalent. a c b d Extremes – a and d Means – b and c In a proportion, the product of the means is equal to the product of the extremes. When using ratios….. If you know only part: 1. Set up a proportion 2. Put the like quantities across from each other 3. Solve…this will give you the other part If you know a total: 1. Make a Let statement and put an X after each number in the ratio 2. Add them to equal the total 3. Solve for x 4. Substitute x in to find the value 1. What is the solution to each proportion? 6 5 a) x 4 b) y4 y 9 3 2. A bonsai tree is 18 in. wide and stands 2 ft tall. What is the ratio of the width of the bonsai to its height? 3. Two complementary angles in the ratio of 2:3. The larger angle measures 54°. Find the measure of the smaller angle. 4. The lengths of the sides of a triangle are in the extended ratio 3:5:6. The perimeter of the triangle is 98 in. What is the length of the longest side? 5. In the diagram, a) x y b) 6 x c) y7 7 x y . What ratio completes the equivalent proportions? 6 7