Visualizing equivalent fractions

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Fractions is a very useful numerical representation of numbers. A fraction is number written in “p/q” form. Where ‘p’ is the numerator and 'q' is the denominator of the fraction. The denominator of a fraction cannot be equal to zero i.e. q not equal to zero. Equivalent means equality. Equivalent fractions are the fractions which when reduced or simplified have the same value. Different mathematical operations such as addition, subtraction, multiplication and division can be used to check for equality for the given fractions. Visualizing the fractions helps solving the fractions easily.
Example 1: Given are two equivalent fractions find the missing value?
3/9 = 1/?
Solution: Given are equivalent fractions. To find the missing number the fraction 3/9 needs to be further simplifies.
The fraction 3/9 can be written as (3 x 1)/ (3 x 3)
Here we have a common number 3 in the numerator and the denominator.
Further simplifying the fraction gives (3 ÷ 3)/ (9 ÷ 3) = 1/3
Hence, the missing number is 3 and the equivalent fraction is 1/3.
Question: Multiple choice question (Pick the correct option.)
What is the fraction 1/3 equivalent to in the following?
a)    2/4       b) 2/3              c) 2/6              d) None of these.
Correct answer: option c.
 Here the given fraction is 1/3. This can be represented as:

One out of thee boxes are shaded. So we have 1 out of 3.
Similarly in 2/6 we have:

Two out of six boxes are shaded. So we can further simplify the fraction 2/6 as follows:
2/6 = (2 x 1)/ (2 x 3) = 1/3. 

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