Fraction Addition Calculator

| Added in Math & Numbers

What is Fraction Addition and Why Should You Care?

Fraction addition is the process of combining two or more fractions into one. Whether you're sharing pizza with friends, adjusting recipes, or managing budgets, adding fractions is a foundational math skill that appears in countless real-world situations.

Mastering fraction addition helps you handle various tasks more accurately and efficiently, from cooking to construction to financial planning.

How to Add Fractions

The process involves these steps:

  1. Find a common denominator - Identify the least common multiple (LCM) of both denominators
  2. Convert the fractions - Rewrite each fraction with the common denominator
  3. Add the numerators - Keep the common denominator
  4. Simplify - Reduce to lowest terms if possible

The Formula

$$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$

Calculation Example

Let's add 2/5 + 3/7:

Step 1: Find the LCM of 5 and 7, which is 35

Step 2: Convert each fraction:

$$\frac{2}{5} = \frac{14}{35}$$

$$\frac{3}{7} = \frac{15}{35}$$

Step 3: Add the numerators:

$$\frac{14}{35} + \frac{15}{35} = \frac{29}{35}$$

The result is 29/35, which is already in simplest form.

Another Example

Adding 1/4 + 1/3:

  • LCM of 4 and 3 is 12
  • 1/4 = 3/12
  • 1/3 = 4/12
  • 3/12 + 4/12 = 7/12

Adding fractions becomes simple when you break it into these manageable steps. This skill helps in everything from cooking to budgeting.

Frequently Asked Questions

To add fractions, find a common denominator, convert each fraction to have that denominator, add the numerators together, and simplify if needed.

A common denominator is a shared multiple of both denominators that allows fractions to be added directly. The least common multiple (LCM) is typically used.

Yes, fractions must have the same denominator before adding. This calculator automatically finds the least common denominator and converts the fractions for you.

Yes, the calculator automatically simplifies the result to its lowest terms by dividing both numerator and denominator by their greatest common divisor.