Fraction Calculator

How to Calculate Fractions

A fraction represents a part of a whole, expressed as one number (the numerator) divided by another (the denominator). Fractions are fundamental in mathematics, cooking, construction, and many real-world measurements.

Fraction Operation Formulas

• Addition: a/b + c/d = (a×d + c×b) / (b×d)
• Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
• Multiplication: a/b × c/d = (a×c) / (b×d)
• Division: a/b ÷ c/d = (a×d) / (b×c)

Simplifying Fractions

To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, 6/8 simplifies to 3/4 because the GCD of 6 and 8 is 2. A fraction is in its simplest form when the numerator and denominator share no common factors other than 1.

Mixed Numbers and Improper Fractions

An improper fraction has a numerator larger than its denominator (e.g., 7/4). It can be converted to a mixed number by dividing the numerator by the denominator: 7/4 = 1 3/4. The whole number is the quotient, and the remainder becomes the new numerator over the original denominator.

Common Fraction Uses

• Cooking: Halving or doubling recipes with 1/2, 1/3, 1/4 cup measurements.
• Construction: Measuring lengths in inches (e.g., 3 5/8 inches).
• Finance: Calculating fractional shares, dividends, and proportions.
• Education: Foundational math skills for algebra and beyond.

Step-by-Step Worked Examples

Walking through a few examples makes the formulas easier to apply by hand. To add 1/4 + 1/3, find a common denominator of 12, convert each fraction (3/12 + 4/12), and add the numerators to get 7/12. To multiply 3/4 × 2/5, multiply the numerators (3 × 2 = 6) and the denominators (4 × 5 = 20), giving 6/20, which simplifies to 3/10. To divide 3/4 ÷ 2/5, multiply by the reciprocal: 3/4 × 5/2 = 15/8, which is 1 7/8 as a mixed number. To subtract 5/6 − 1/2, use a common denominator of 6: 5/6 − 3/6 = 2/6, which simplifies to 1/3. The calculator shows each of these steps so you can follow along and verify your own working.

Finding Common Denominators

Adding or subtracting fractions requires a shared denominator. The simplest approach is to multiply the two denominators together, but that can produce large numbers. A cleaner method is to use the least common multiple (LCM) of the denominators. For example, to add 5/12 + 7/18, the LCM of 12 and 18 is 36, so convert to 15/36 + 14/36 = 29/36. Using the LCM keeps the numbers smaller and the result closer to its simplified form. The calculator handles this automatically, but understanding the process helps you check results and build number sense.

Converting Between Fractions, Decimals, and Percentages

Fractions, decimals, and percentages are three ways of expressing the same value. To convert a fraction to a decimal, divide the numerator by the denominator: 3/4 = 0.75. To convert a decimal to a percentage, multiply by 100: 0.75 = 75%. To convert a percentage to a fraction, write it over 100 and simplify: 75% = 75/100 = 3/4. This calculator displays the decimal equivalent alongside the simplified fraction and mixed number, so you can see all three representations at once. That is especially useful when comparing prices, proportions, or measurements that use different formats.

Tips for Working with Fractions

Always simplify your final answer — an unsimplified fraction is technically correct but harder to read and compare. When adding or subtracting, find the least common denominator to keep the arithmetic manageable. When multiplying, you can simplify before multiplying by canceling common factors between any numerator and any denominator, which reduces the size of the numbers. When dividing, remember that you are multiplying by the reciprocal — never divide by zero, as the result is undefined. For negative fractions, keep the sign in the numerator and treat the denominator as positive to avoid confusion. The calculator enforces all of these rules and flags invalid inputs such as a zero denominator.