Decomposing fractions

Decomposing fractions 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. Correct answer: option b. 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.