6.16.2 ratio + proportion.notebook November 18, 2014 11/18/14- Warm Up Problem Write each fraction in simplest terms. Nov 157:06 PM 1 6.16.2 ratio + proportion.notebook November 18, 2014 Nov 189:34 AM 2 6.16.2 ratio + proportion.notebook November 18, 2014 Section 6.1-6.2 - Ratios and Proportions Goals: write and simplify ratios, solve proportions and problems involving proportions, use the properties of proportions Ratio: a comparison of two quantities Example: 2/3 or 2:3 * a ratio should always be written in simplest terms * What is the ratio of boys to girls in the class? What is the ratio of teachers to students in the class? What is the ratio of people who think geometry is awesome to people who don't? Nov 157:32 PM 3 6.16.2 ratio + proportion.notebook November 18, 2014 Proportion: an equation stating that two ratios are equal Example: Names for parts of a proportion Extremes: values in the upper left and lower right positions of the proportion Means: values in the lower left and upper rignt positions of the proportion 3 6 = 4 8 Nov 157:53 PM 4 6.16.2 ratio + proportion.notebook November 18, 2014 Cross-Products Property 1. If , then Cross-Multiplying Solving a proportion means finding the value of the variable that makes the proportion true • mutliply the extremes • multiply the means • solve the resulting equation 3 x = 5 75 4 = x 6 18 Nov 158:00 PM 5 6.16.2 ratio + proportion.notebook November 18, 2014 Solve by Cross Multiplying • cross multiply • use distributive property when one of the means or extremes has two terms x + 1 2x 3 3 = 5 Nov 166:26 PM 6 6.16.2 ratio + proportion.notebook November 18, 2014 Other Properties of Proportions 2. If 2 ratios are equal, then their reciprocals are also equal. 3. If you interchange the means of a proportions, then you form another true proportion. 4. In a proportion, if you add the value of each ratio's denominator to its numerator, then you form another true proportion. This is a true proportion. Write three more. 2 6 = 5 x Nov 173:07 PM 7 6.16.2 ratio + proportion.notebook November 18, 2014 Write and Solve a Proportion An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog. Nov 1510:13 PM 8 6.16.2 ratio + proportion.notebook November 18, 2014 Write and Solve a Proportion When making the movie Star Wars, a model was used to film the explosion of the Death Star. The real Death Star supposedly had a diameter of 3,500 km. If the model was built using the scale 50 km = 1 cm, what was the diameter of the model? Nov 1512:08 PM 9 6.16.2 ratio + proportion.notebook November 18, 2014 Assignment: 6.1-6.2 Worksheet Nov 1512:14 PM 10
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