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?
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.
Explanation: The fraction 7/11 needs to be decomposed.
In option b: 5/11 + 2/11 (Here 11 is the common denominator so the numerators of the fractions can be added.)
This gives, 5/11 + 2/11 = (5 + 2)/11 = 7/11.