Constructing proportions to solve application problems

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Ratio and proportion is one of the basic topics in math. Proportion is constructed to solve word problems or a questions where quantities maintain a fixed ratio or the same fractional value. . In such cases the question can be analyzed and the fixed ratio can be calculated. 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. When things are in proportion their relative sizes are the same.
Example 1: Do these form ratio and proportion?
A basket has10 apples and 5 oranges.
Another basket has 30 apples and 15 oranges.
Solution: The number of apples and oranges in the baskets are to be compared. The ratio can be expressed as:
First basket: Number of apples/ Number of oranges = 10/5 = 2/1.
Second basket: Number of apples/ Number of oranges = 30/15 = 2/1.
The ratios are the same hence they form a proportion.
Question: Multiple choice question (Pick the correct option.)
Find the k in the proportion k : 3 = 4 : 3?
a)    3          b) 12               c) 4                 d) None of these.
Correct answer: option c
Explanation: The proportion can be expressed in a fraction in the form.
This gives, k/3 = 4/3.
Now multiply both sides of the equation by 3.
This gives 3(k/ 3) = (4/3) * (3); k = 4.
Hence the value of k for the given proportion is 4.

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