You must be familiar with the concept of fractions; in this section, we will learn how fractions are split up or divided into smaller fractions forming decomposed fractions.
We will be learning the methods of decomposing fractions and mixed fractions. This study is done with the help of several examples so that the students understand the concept of decomposing fractions in an effective manner.
What Is Meant by Decomposing Fractions?
Decomposition of fractions
In real terms, the meaning of decompose means ‘splitting up’ or ‘dividing the fractions into smaller parts or chunks. When we decompose a fraction, we divide it into smaller fractions. It is to be noted that the decomposed fractions or the smaller fractions add up to form the initial fraction.
How Can You Decompose Fractions?
We can decompose fractions by breaking them into unit fractions.
What Are Unit Fractions?
Unit fractions are those fractions in which the numerator is 1. For example - ⅓, ⅕, etc. This means that a unit fraction is a part of a whole unit or a part of 1.
Larger Fractions into Many Unit Fractions
The easiest way to break larger fractions is by decomposing them into many unit fractions. Like ⅝ is the same as ⅛, ⅛, ⅛, ⅛, ⅛, which is fives times ⅛. Let us take another example. Consider the fraction ⅚; this means there are 5 parts among 6 parts in total. This can be decomposed as ⅙, ⅙, ⅙, ⅙, ⅙.
Sum of Smaller Fractions That Are Not Unit Fractions
There is yet another way to decompose larger fractions. We can decompose a large fraction into smaller fractions. This method of decomposition of large fractions into smaller ones can be applied where we cannot decompose the larger fraction into unit fractions, as observed in the previous section.
We can also decompose a fraction by using the sum of smaller fractions.
Like - ⅚ can also be split into 1⁄6, 1⁄6, and 3⁄6 or 2⁄6 and 3⁄6 or 1⁄6 and 4⁄6
Another example - 5⁄6 = 2⁄6 + 3⁄6 = 1⁄3 + 1⁄2
Here, we can again simplify the fraction as 2⁄6 = 1⁄3 and 3⁄6 = 1⁄2
Decomposing Mixed Fractions
A mixed fraction is a combination of a whole number and a proper fraction, which is represented together. The mixed fraction represents a number that is between any two of the whole numbers.
The numerator and denominator in the mixed fraction are a part of the proper fraction, thereby forming the mixed number. The result, after we split a mixed fraction, is a whole number and a proper fraction.
Conclusion
One can study the decomposition of fractions only with a proper understanding of fractions. For parents, in order to help their kids, it's always advisable to use images and other visual representations which will help them to grasp the method of decomposition.
Also, another note to remember, while working with fractions, you can only add or subtract the parts which refer to the same size or the whole.
FAQs on Decomposing of Fractions
1. What does it mean to decompose a fraction in Maths?
In mathematics, to decompose a fraction means to break it down into the sum of two or more smaller, simpler fractions. For instance, the fraction 5/8 can be broken down into 2/8 + 3/8. The total value remains the same, but it is expressed as a sum of its parts.
2. What are the common methods to decompose a proper fraction?
There are two primary methods for decomposing a proper fraction:
- Using Unit Fractions: A unit fraction is a fraction with 1 as the numerator (e.g., 1/6). You can break down a fraction into a sum of unit fractions. For example, 4/6 can be decomposed as 1/6 + 1/6 + 1/6 + 1/6.
- Using a Sum of Smaller Fractions: You can also break it down into any combination of smaller fractions that add up to the original. For example, 4/6 can also be decomposed as 1/6 + 3/6 or 2/6 + 2/6.
3. Can you show an example of decomposing the fraction 3/4?
Certainly. The fraction 3/4 can be decomposed in multiple ways. Here are two examples:
- Decomposition into unit fractions: 3/4 = 1/4 + 1/4 + 1/4
- Decomposition into other smaller fractions: 3/4 = 1/4 + 2/4
Both sums correctly add up to the original fraction, 3/4.
4. How do you decompose an improper fraction or a mixed number?
To decompose a mixed number, you first convert it into an improper fraction. For example, the mixed number 1 ½ is converted to 3/2. Once you have the improper fraction, you can decompose it just like a proper fraction. For 3/2, the decomposition would be 1/2 + 1/2 + 1/2.
5. Why is learning to decompose fractions important?
Decomposing fractions is a fundamental skill that helps in several ways. It makes complex fraction addition and subtraction easier to understand by breaking problems into smaller parts. It also provides a strong visual and conceptual foundation for understanding that numbers can be represented in different, flexible forms, which is a key concept in higher mathematics like algebra.
6. Is composing a fraction simply the reverse of decomposing it?
Yes, precisely. Composing a fraction is the process of adding smaller fractions together to create a single, larger fraction. For example, if you are asked to compose a fraction from 1/8 + 3/8, you would add them together to get 4/8. It is the same process as standard fraction addition, which is the opposite of breaking a fraction apart (decomposing).
7. How is decomposing simple fractions related to 'Partial Fractions' in higher classes?
Decomposing simple fractions in primary school and using partial fractions in higher classes (like Class 11 or 12) are based on the same core idea: breaking something complex into simpler parts. In primary classes, we decompose number fractions like 7/8 into 3/8 + 4/8. In higher mathematics, the same principle is applied to complex algebraic fractions to make them easier to work with in topics like calculus and integration.
