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What Is a Fraction?

A fraction represents a part of a whole. It has two parts:

• Numerator (top number): shows how many parts we have.
• Denominator (bottom number): shows how many equal parts the whole is divided into.

For example:
3/4 means 3 out of 4 equal parts.

Types of Fractions

Before learning how to add fractions, it’s important to understand the types:

1. Like Fractions – Fractions with the same denominator (e.g., 1/5 and 2/5).
2. Unlike Fractions – Fractions with different denominators (e.g., 1/3 and 1/4).

How to Add Fractions with the Same Denominator

This is the easiest case. When denominators are the same, just add the numerators and keep the denominator unchanged.

Formula:
a/b + c/b = (a + c)/b

Example 1:

1/5 + 2/5 = (1 + 2)/5 = 3/5

No need to change anything. Just add the top numbers (1 + 2) and keep the bottom number (5) the same.

How to Add Fractions with Different Denominators

This is a little more complex. You need to make the denominators the same before you can add them. Here’s the step-by-step method:

Step 1: Find the Least Common Denominator (LCD)

• The LCD is the smallest number that both denominators can divide evenly into.

Step 2: Convert the fractions

• Adjust the fractions so they both have the LCD as the denominator.

Step 3: Add the new numerators

• Once the denominators are the same, add the numerators.

Step 4: Simplify the fraction (if needed)

Example 2: Add 1/3 + 1/4

Step 1: Find LCD

• The LCD of 3 and 4 is 12

Step 2: Convert both fractions

• 1/3 = 4/12 (multiply top and bottom by 4)
• 1/4 = 3/12 (multiply top and bottom by 3)

Step 3: Add the new fractions

• 4/12 + 3/12 = 7/12

Final Answer: 7/12

Tip: Use Cross-Multiplication (Shortcut Method)

For quick addition of two fractions:

a/b + c/d = (ad + bc) / bd

Example 3:

2/3 + 1/5

• (2×5 + 1×3) / (3×5) = (10 + 3) / 15 = 13/15

This method is useful but may require simplifying at the end.

Adding Mixed Numbers

A mixed number is a whole number plus a fraction (e.g., 2 1/3).

Steps:

1. Convert mixed numbers to improper fractions.
2. Follow the same steps to add.
3. Convert back to a mixed number (if needed).

Example 4:

1 1/2 + 2 2/3

Step 1: Convert to improper fractions

• 1 1/2 = 3/2
• 2 2/3 = 8/3

Step 2: Find LCD

• LCD of 2 and 3 is 6
• 3/2 = 9/6
• 8/3 = 16/6

Step 3: Add

• 9/6 + 16/6 = 25/6

Step 4: Convert to mixed number

• 25 ÷ 6 = 4 with remainder 1 → 4 1/6

Tips to Remember

• Always find a common denominator before adding.
• Simplify your answer whenever possible.
• If dealing with mixed numbers, convert to improper fractions first.
• Practice with real-life examples: cutting pizza, measuring ingredients, dividing money, etc.

Practice Problems

Try solving these on your own:

1. 3/8 + 1/8 = ?
2. 2/5 + 1/3 = ?
3. 1 1/4 + 2 2/5 = ?
4. 5/6 + 2/9 = ?

(Answers at the bottom of this article)

Why Is Learning How to Add Fractions Important?

Adding fractions is not just a school task. It’s used in:

• Cooking (e.g., 1/2 cup + 1/4 cup)
• Construction (e.g., measuring inches and feet)
• Budgeting (e.g., splitting bills or discounts)
• Everyday decisions (e.g., combining times or distances)

Mastering fractions builds your confidence and helps you solve real-world problems.