# Decomposing fractions

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Learning about fractions is one of the basic and important topics in math. 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. Decomposing a fraction means writing a fraction as a combination of two or more fractions. Different mathematical operations such as addition and subtraction can be used to decompose a fraction into different fractions with the same denominator.

Example 1: Decompose the fraction 5/7 into sum of two fractions if one of them is 3/7 find the other?
Solution: Given is the fraction 5/7 which needs to be decomposed.
Here one of the fraction is 3/7 so, 5/7 = ---- + 3/7.
The other fraction which needs to be found.
The decomposition can be represented as the following.
The fraction 5/7 (Five shaded regions out of seven.)
The fraction 3/7 (Three shaded regions out of seven.)

Hence, the fraction can be decomposed as 5/7 = 3/7 + 2/7.

Question: Multiple choice questions (Pick the correct option.)
Which of the following is the decomposition of the fraction 7/11?
a)    5/11 + 3/11                b) 5/11 + 2/11            c) 5/11 + 4/11            d) None of these.