Fraction Calculator

How to use this fraction calculator

Each tool on this page solves a specific fraction problem. Choose the calculator that matches your task, enter your values, and click Calculate. Results appear in simplified form — as an improper fraction, mixed number, or decimal when relevant — with a short explanation of the steps.

1. Basic fractions: Enter two numerators and denominators, pick +, −, ×, or ÷, then calculate.
2. Mixed numbers: Type values like 2 3/4 or -1 1/2 in the mixed-number tool.
3. Simplify: Enter a whole number (optional) plus numerator and denominator to reduce to lowest terms.
4. Convert: Use the decimal-to-fraction or fraction-to-decimal tools for quick conversions.
5. Large numbers: Use the big-number tool when numerators or denominators exceed normal calculator limits.

For a deeper walkthrough, read our guide: How to Simplify Fractions.

What is a fraction?

In mathematics, a fraction represents a part of a whole. It has a numerator (top) and a denominator (bottom). For example, in 38, 3 is the numerator and 8 is the denominator — three parts out of eight equal parts.

The denominator cannot be zero because division by zero is undefined. Fractions can be proper (numerator smaller than denominator) or improper (numerator equal to or larger than denominator). Improper fractions can be written as mixed numbers, such as 134.

Types of fractions

Understanding fraction types helps you choose the right format for your answer:

• Proper fraction: Numerator is less than the denominator (e.g. 38). Value is between 0 and 1.
• Improper fraction: Numerator is equal to or greater than the denominator (e.g. 74). Value is 1 or more.
• Mixed number: A whole number plus a proper fraction (e.g. 134).
• Equivalent fractions: Different fractions with the same value, such as 12 and 24.

Our simplify tool reduces any fraction to its unique lowest-terms form using the GCF (GCD).

Addition

To add fractions, find a common denominator, convert each fraction, then add the numerators:

Example: 34 + 16 = 1824 + 424 = 2224 = 1112

An efficient alternative is to use the least common multiple (LCM) of the denominators as the common denominator instead of the product.

Subtraction

Subtract fractions the same way as addition — find a common denominator, then subtract numerators:

Example: 56 − 14 = 1012 − 312 = 712

Multiplication

Multiply numerators together and denominators together — no common denominator needed:

Example: 34 × 16 = 324 = 18

Division

Divide by multiplying the first fraction by the reciprocal of the second:

Example: 34 ÷ 16 = 34 × 61 = 184 = 92

Simplification

A fraction is in simplest form when the numerator and denominator share no common factors other than 1. Divide both by their GCD to simplify. Our calculators return results in both improper fraction and mixed-number form when appropriate.

Converting between fractions and decimals

To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a fraction, write the decimal over a power of 10 (or use continued fractions) and simplify. Example: 0.375 = 3751000 = 38.

Repeating decimals (like 0.333…) can be written as exact fractions: 0.3 recurring = 13. For repeating patterns, use our fraction tools with rounded inputs or work through the pattern manually.

Comparing and ordering fractions

To compare fractions with different denominators, convert them to equivalent fractions with a common denominator, or compare their decimal values. Example: Is 35 greater than 23? Convert: 915 vs 1015 — so 23 is larger.

On number lines and in real data, converting to decimals or using the LCM calculator for a common denominator makes ordering straightforward.

Real-world uses of fractions

Fractions appear in everyday life and professional work:

• Cooking & baking: Scaling recipes — doubling 34 cup of flour means multiplying by 2.
• Construction & DIY: Measuring lumber, tile spacing, and pipe lengths in inches and fractions of an inch.
• Probability: A 1-in-6 chance is 16; use our probability calculator for more events.
• Education: Homework, standardized tests, and grade calculations often require fraction arithmetic.
• Finance: Interest rates, profit shares, and ownership splits are often expressed as fractions or percentages — see our percentage calculator.

Frequently Asked Questions

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