Addition and Subtraction of Fractions

Fractions are a way of representing numbers that are not whole numbers. They express parts of a whole. In Class 5 Maths, it is essential to understand addition and subtraction of fractions. This explanation will guide you through the process of adding and subtracting fractions in an easy and detailed manner.

What is fraction?

A fraction is a number that looks like a/b, where a is the numerator (the top number), and b is the denominator (the bottom number). The denominator shows how many parts the whole is divided into, and the numerator shows how many of those parts we have.

Visual example of fractions

A fraction like 3/4 is represented like this:

The shaded parts represent the numerator 3, and the total number of parts into which the whole is divided is represented by the denominator 4.

Finding common denominators

To add or subtract fractions, the first step is to make sure the fractions have the same denominator. This is called finding a common denominator. Let's say we have two fractions:

1/3
1/4

Here's how we can find a common denominator:

• Identify the denominators of the fractions. In this case, they are 3 and 4.
• The least common multiple (LCM) of 3 and 4 is 12. This becomes the common denominator.

Visual example: Converting to common denominators

1/3 = 4/12
1/4 = 3/12

Adding fractions

Once the denominators of the fractions are the same, you can simply add the numerators. The denominators will remain the same. For example, using the fractions from before:

4/12 + 3/12 = (4 + 3)/12 = 7/12

The fractions 4/12 and 3/12 add up to 7/12.

Visual example: Adding fractions

Subtracting fractions

Subtracting fractions is similar to adding them, but instead of adding the numerators, you subtract them. The denominator remains the same:

4/12 - 3/12 = (4 - 3)/12 = 1/12

This time, subtracting 3/12 from 4/12 gives the result 1/12.

Visual example: Subtracting fractions

Practical example

Example 1: Adding fractions

Let's add these fractions: 2/5 + 1/2.

1. First, convert the fractions to a common denominator. The LCM of 5 and 2 is 10.
   • 2/5 = 4/10
   • 1/2 = 5/10
2. Add: 4/10 + 5/10 = 9/10

Example 2: Subtracting fractions

Subtract these fractions: 3/4 - 1/3.

1. First, find a common denominator. The LCM of 4 and 3 is 12.
   • 3/4 = 9/12
   • 1/3 = 4/12
2. Subtract: 9/12 - 4/12 = 5/12

Key takeaways

• Fractions represent parts of a whole. The numerator tells how many parts there are, and the denominator tells how many parts the whole is divided into.
• To add or subtract fractions, they must have the same denominator. This is called finding the common denominator, often by finding the least common multiple (LCM) of the denominators.
• When the denominators of the fractions are equal, you can add or subtract the numerators. The denominator remains unchanged.
• After you perform the addition or subtraction, simplify the fraction if possible.

Understanding addition and subtraction of fractions combines the ability to find common denominators with the arithmetic operations of adding and subtracting fractions. Mastering these skills ensures a solid arithmetic foundation for solving problems involving fractions.

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