Adding fractions with common denominators

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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 number. The denominator of a fraction cannot be equal to zero i.e. q not equal to zero. Different mathematical operations can be used to simplify and solve a fractions such as addition, subtraction, multiplication and division. While adding fractions there should always be a common denominator. Here are some examples for adding fractions with a common denominator.

Example 1: Simplify and find the answer by adding the given fraction numbers 2/5 + 3/5 + 4/5?

Solution: The first step is to check the denominator of the given fractions. We have a common denominator of 5 for all three fractions.
Since the denominator of the fractions is same, add the numerators of the given fractions.
This gives 2/5 + 3/5 + 4/5 = (2 + 3 + 4) / 5 = 9/5.

Therefore, the answer for 3/4 + 5/4 + 1/4 = 9/5.

Question: Multiple choice question (Pick the correct option.)
What is the answer for adding the two fractions 1/7 + 6/7?
a)    1          b) 6/7              c) 5/7              d) None of these. 

Correct answer: option a.

Here the fractions 1/7 and 6/7 have the same denominator 7. Since we have the common denominator we can add the numerators.
This gives 1/7 + 6/7 = (1 + 6) /7 = 7/7.
The fraction 7/7 can be further simplified. Hence 7/7 = 1.

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