Solving ratio problems with tables

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Ratio is one of the very often used topics in mathematics. Ratio is defined as the comparison between quantitates or numbers. The symbol for the representing ratio is “:”. Ratio helps in solving questions related to comparisons, proportions and many other word problems.  For example, a / b can be written as a : b. Here a/b is fraction form and a:b is the ratio form. The ratio can be simplifies if a and b have any common factors. 

Example 1: Fill in the blanks if the table below?

Solution: The table given have set of equivalent ratio.
The first ratio given is 6: 5.
The second ratio given is 12: 10. This can be obtained by the first ratio.
Write the ratio 6: 5 as a fraction (6/5) x (2/2) = 12/10.
In the third ratio 18 can be obtained by multiplying 6 x 3 = 18.
So multiplying the ratio 6: 5 by 3 gives (6/5) x (3/3) = 18/15.
Hence writing as a ratio = 18: 15.
Therefore the missing blank is 15.
Question: Multiple choice question (Pick the correct option.)
In the given table below the missing number in the ratio is?

a)    28                    b) 16               c) 14               d) None of these.
Correct answer: option a.
Explanation: The table given have set of equivalent ratio.
The first ratio given is 4: 7 or 4/7.
In the third ratio 16 can be obtained by multiplying 4 x 4 = 16.
So multiplying the ratio 4: 7 by 4 gives (4/7) x (4/4) = 16/28.

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