Adding & Subtracting Fractions

Perform basic arithmetic on fractions with simplified results.

2026-05-12T10:30:54.830Z

Select Operation

Result

0.833333

What is Fraction Addition & Subtraction?

Adding and subtracting fractions requires a common denominator. This is because you can only combine "like" parts. For example, you can't directly add half an apple to a third of an apple without finding a common unit.

Subtraction follows the same logic as addition: find the common denominator, adjust the numerators, and then subtract the second numerator from the first.

Standard Fractions Only: This calculator works with fractions where the numerator and denominator are both whole numbers (integers). Enter positive or negative integers only—no decimals or mixed numbers. For example, enter 3/4 or -5/2, but not 3.5/2 or 2¾.

How to Add & Subtract Fractions

The Formulas

Addition

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

Subtraction

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

Note: In these formulas, a, b, c, and d are all integers. This calculator enforces integer inputs to ensure standard, exact fraction arithmetic.

Step-by-Step Method

1.Find a common denominator by multiplying the two denominators.
2.Adjust the numerators by cross-multiplying (a*d and c*b).
3.Add or subtract the new numerators together.
4.Simplify the resulting fraction if possible.

Worked Example

Problem: Subtract 1/3 from 1/2

Step 1:Identify the denominators: 2 and 3

Step 2:Find common denominator: 2 × 3 = 6

Step 3:Cross-multiply numerators: (1 × 3) - (1 × 2) = 3 - 2 = 1

Answer:1/6 = 0.1667

Frequently Asked Questions

Why can't I use decimals for numerators or denominators?

This calculator is designed for standard fraction arithmetic, where numerators and denominators are integers. Using decimals would create rational expressions rather than true fractions. For example, 3.5/2 is technically (7/2)/2, which is more complex. If you need to work with decimal values, convert them to fractions first (e.g., 3.5 = 7/2) and enter the integer parts separately.

What is the Least Common Denominator (LCD)?

The LCD is the smallest number that all denominators can divide into evenly. Using the LCD keeps the numbers smaller and easier to work with.

Can the result be negative?

Yes, if you subtract a larger fraction from a smaller one, the result will be a negative fraction.

Do I always need to simplify?

While not strictly required for correctness, simplifying makes the fraction much easier to understand and compare.

What if one number is a whole number?

Treat the whole number as a fraction with a denominator of 1. For example, 5 becomes 5/1.

How do I find the LCD faster?

For simple fractions, multiply the denominators. For more complex cases, find the least common multiple (LCM) of the denominators.

Can I add or subtract more than two fractions?

Yes! Find the LCD for all denominators, then add or subtract all fractions at once.

How do improper fractions affect addition and subtraction?

Improper fractions (numerator > denominator) work the same way. You can add 7/3 + 2/5 normally and get an improper result that can be converted to a mixed number.