Analyzing and identifying proportional relationships

Analyzing and identifying proportional relationships Proportion is a useful topic in math. Proportions can be is identified when the quantities maintain a fixed ratio or the same fractional value. Proportionality always maintains a fixed ratio or fraction between two quantities. For example, a / b = c / d. It can be written as a : b = c : d. Proportion is often used in the word problems. In such cases the question can be analyzed and the fixed ratio can be calculated. Example 1: George took 5 quizzes in 2 two weeks of school. How many quizzes will he take in 6 week of school in the same proportion? Solution: Here given is 5 quizzes are taken in 2 weeks of school. The ratio can be expressed as: Number of quizzes/ Number of weeks = 5/2. In the same proportion for 6 weeks: Number of quizzes/6 = 5/2. This gives, number of quizzes = 5/2 x 6 = 30/2 = 15. Hence George takes 15 quizzes in 3 weeks. Question: Multiple choice question (Pick the correct option.) Find the m in the proportion m : 8 = 7 : 4? a) 5 b) 12 c) 14 d) None of these. Correct answer: option c Explanation: The proportion can be expressed in a fraction in the form. This gives, m/8 = 7/4. Now multiply both sides of the equation by 7. This gives 7(m/ 7) = (7/4) * (8); m = 7 * 2 = 14. Hence the value of m for the given proportion is 14.