Fraction Calculator

What is a Fraction?

A fraction represents a part of a whole. It shows how many parts of a divided whole we are taking.

A fraction has two main parts:

Numerator (top number): Tells how many parts we are taking.
Denominator (bottom number): Tells into how many equal parts the whole is divided.

Example: In 3/4
• 3 is the numerator → we take 3 parts
• 4 is the denominator → the whole is divided into 4 equal parts

Types of fractions:

Proper Fraction: Numerator < Denominator (e.g., 2/3, 5/8)
Improper Fraction: Numerator ≥ Denominator (e.g., 7/3, 5/2)
Mixed Number: Whole number + proper fraction (e.g., 2 1/3)

What is a Fraction Calculator?

A fraction calculator is an online or app-based tool that helps you perform operations with fractions quickly and accurately. It shows step-by-step solutions, making it easier to learn.

It can handle:

Adding, subtracting, multiplying, and dividing fractions
Converting between fractions, decimals, and mixed numbers
Simplifying fractions automatically

Operations on Fractions - With Steps & Formulas

1. Adding Fractions

Rule:
• Same denominators: (a/b) + (c/b) = (a + c)/b
• Different denominators: Find the Least Common Denominator (LCD), convert, then add numerators.

Example 1: 1/2 + 1/3

Step 1: LCD of 2 and 3 is 6
Step 2: Convert → 1/2 = 3/6, 1/3 = 2/6
Step 3: Add → (3 + 2)/6 = 5/6

Example 2 (Same denominator): 3/4 + 2/4 = (3 + 2)/4 = 5/4 = 1 1/4

2. Subtracting Fractions

Rule:
Same as addition, but subtract the numerators.

Example: 3/4 - 1/6

Step 1: LCD of 4 and 6 is 12
Step 2: Convert → 3/4 = 9/12, 1/6 = 2/12
Step 3: Subtract → (9 - 2)/12 = 7/12

3. Multiplying Fractions

Rule (Very Easy):
(a/b) × (c/d) = (a × c) / (b × d)
No need for common denominator. Simplify before or after multiplying.

Example: 2/3 × 4/5

Multiply numerators: 2 × 4 = 8
Multiply denominators: 3 × 5 = 15
Result: 8/15 (already simplified)

Example with cancellation: 3/4 × 2/9 = (3×2)/(4×9) = 6/36 = 1/6

4. Dividing Fractions

Rule (Keep-Change-Flip):
(a/b) ÷ (c/d) = (a/b) × (d/c)
Flip the second fraction and multiply.

Example: 3/4 ÷ 2/5

Step 1: Flip 2/5 → 5/2
Step 2: Multiply → (3/4) × (5/2) = 15/8
Result: 15/8 or 1 7/8

Another Example: 1/2 ÷ 1/4 = (1/2) × (4/1) = 2

Quick Tips for Success

Always simplify the final answer by dividing numerator and denominator by their Greatest Common Divisor (GCD).
Convert mixed numbers to improper fractions before calculations: e.g., 2 1/3 = (2×3 + 1)/3 = 7/3
For addition and subtraction, find the Least Common Multiple (LCM) of denominators to get the LCD.
Use a fraction calculator to check your work and see step-by-step solutions.

Related: Percentage Calculator