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Definition: A ratio is a comparison using ___________________. The ratio of a to b can be written in 2 ways: either ________ or _________. Ratios are always expressed in _________________ form. Example 1: In Logan’s high school, there are 190 teachers and 2660 students. What is the student to teacher ratio at his school? Sometimes we use the idea of an extended ratio: ______________________________ Example 2: a) The ratio of the measures of the angles in a triangle is 3:4:5. Find the measures of the angles. b) The ratio of the measures of the sides of triangle is 2:3:3 and the perimeter of the triangle is 392 cm. Find the length of the longest side of the triangle. You try: 1. The number of students that participate in sports programs at Central HS is 520. The total number of students in the school is 1850. What is the approximate athlete-to-student ratio at the school? 2. A triangle’s angle measures are in the extended ratio of 1:3:5. Find each angle. An idea closely related to ratios is the term proportion. What is a proportion? ___________________________________________________ a c In the proportion , b and c are called the ______________ b d a and d are called the _______________ The product of the means _____________ the product of the extremes. We refer to each of them as the “_______ - ____________” Example 3: Solve each proportion. 6 21 x 3 4x a) b) x 31.5 2 5 c) 4 x 5 26 3 6 Example 5: Monique randomly surveys 30 students from her Geometry class and finds that 18 of them have a pet dog or cat. If there are 870 students at Monique’s school, predict the total number of students with a pet dog or cat. You try: Fernando surveyed 50 students at his school and found that 18 of them drove their own car to school. If 378 students drive their own car to school, predict how many students attend Fernando’s school.