How to Decompose Fractions?

A Step-by-step guide to decomposing fractions

Decomposing involves ‘breaking up’ or ‘dividing something into littler parts’.

Decomposing fractions refers to the process of breaking down a given fraction into the sum of smaller fractions. Here’s a step-by-step guide to decomposing fractions:

Step 1: Choose the fraction to decompose

Select the fraction you want to decompose. For this example, let’s use 4/6.

Step 2: Simplify the fraction

Before decomposing, it’s helpful to simplify the fraction if possible. Find the greatest common divisor (GCD) of the numerator and denominator, and divide both by the GCD. In our example, the GCD of 4 and 6 is 2. 4/6 ÷ 2/2 = 2/3

Step 3: Choose a decomposition method

There are several methods for decomposing fractions, such as decomposing into unit fractions or using a common denominator. For this example, let’s decompose the simplified fraction (2/3) into unit fractions.

Step 4: Decompose the fraction

To decompose 2/3 into unit fractions, determine which unit fractions add up to the given fraction. In our example, 2/3 can be represented as the sum of two 1/3 unit fractions: 2/3 = 1/3 + 1/3

Step 5: Alternative decompositions (optional)

You can also decompose the fraction using a different method, such as using a common denominator. For instance, you can represent 2/3 as the sum of fractions with a common denominator of 6: 2/3 = 1/2 + 1/6

Step 6: Confirm the result

Verify that the sum of the smaller fractions equals the original fraction. In our examples, both decompositions are correct as 1/3 + 1/3 = 2/3 and 1/2 + 1/6 = 2/3.

Remember that there can be multiple valid decompositions for a given fraction. By practicing different methods and exploring various decompositions, you’ll gain a deeper understanding of how fractions can be broken down into smaller parts.

Decomposition of Fractions-Example 1:

How do you write \(\frac{3}{8}\) as a sum of two fractions?

Solution: To express the fraction as the sum of two different fractions, we can divide the number three into \(1\) and \(2\).

\(\frac{3}{8}=\frac{1}{8}+\frac{2}{8}\)

Exercises for Decomposition of Fractions

Write the fraction as the sum of two equal fractions.

1. \(\color{blue}{\frac{5}{11}}\)
2. \(\color{blue}{\frac{7}{4}}\)
3. \(\color{blue}{\frac{4}{6}}\)

1. \(\color{blue}{\frac{3}{11}+\frac{2}{11}}\)
2. \(\color{blue}{\frac{4}{4}+\frac{3}{4}}\)
3. \(\color{blue}{\frac{2}{6}+\frac{2}{6}}\)