Analyzing and identifying proportional relationships

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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.

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