Equivalent fractions

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Equivalent means equality. Equivalent fractions are the fractions which when reduced or simplified have the same value. Fractions are a very commonly used 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. Different mathematical operations such as addition, subtraction, multiplication and division can be used to simplify, solve and check for equality for the given fractions.
 
Example 1: Given are two equivalent fractions find the missing value?

5/10 = 1/?

Solution: Given are equivalent fractions. To find the missing number the fraction 5/10 needs to be further simplifies.

The fraction 5/10 can be written as (5 x 1)/ (2 x 5)

Here we have a common number 5 in the numerator and the denominator.

Further simplifying: (5 ÷ 5)/ (10 ÷ 5) = 1/2.

Hence, the missing number is 2 and the equivalent fraction is 1/2.
 
Question: Multiple choice question (Pick the correct option.)

What is the fraction 6/12 equivalent to in the following?

a)    3/8       b) 2/3              c) 1/2              d) None of these.

Correct answer: option c.

Explanation: Given is the fraction 6/12. The fraction can be further simplified as follows:
The fraction 6/12 can be written as (6 x 1)/ (6 x 2)

Here we have a common number 6 in the numerator and the denominator.
Further simplifying: (6 ÷ 6)/ (12 ÷ 6) = 1/2.

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