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Fraction Calculator

I built this tool to make fraction math simple. Add, subtract, multiply, or divide any combination of fractions and mixed numbers with ease.

Quick Answer

To add or subtract fractions, use a common denominator; to multiply, multiply tops and bottoms; to divide, flip the second fraction and multiply. For example, 1/2 + 1/3 = 5/6.

Enter two fractions and an operation above to get the answer, simplified to lowest terms.

Fraction Calculator

Add, subtract, multiply, or divide fractions and mixed numbers.

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Understanding Fraction Calculations

Fractions represent parts of a whole. This calculator handles various operations with proper fractions, improper fractions, and mixed numbers.

Types of Fractions

  • Proper Fraction: Numerator is smaller than the denominator (e.g., 1/2, 3/4).
  • Improper Fraction: Numerator is greater than or equal to the denominator (e.g., 3/2, 5/5).
  • Mixed Number: A whole number and a proper fraction combined (e.g., 1 1/2, which is 3/2).

This calculator first converts any mixed numbers into improper fractions to perform calculations.

Adding Fractions (a/b + c/d)

Method: To add fractions, they must have a common denominator. If denominators are different, find a common multiple (often the product of the two denominators for simplicity, though least common multiple is more efficient).

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

Example: 1/2 + 1/3

  1. (1*3 + 2*1) / (2*3)
  2. (3 + 2) / 6
  3. Result: 5/6

Subtracting Fractions (a/b - c/d)

Method: Similar to addition, find a common denominator.

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

Example: 1/2 - 1/3

  1. (1*3 - 2*1) / (2*3)
  2. (3 - 2) / 6
  3. Result: 1/6

Multiplying Fractions (a/b * c/d)

Method: Multiply the numerators together and the denominators together.

Formula: (a/b) * (c/d) = (ac) / (bd)

Example: 1/2 * 2/3

  1. (1*2) / (2*3)
  2. 2 / 6
  3. Simplify by dividing numerator and denominator by their greatest common divisor (2): 1/3

Dividing Fractions (a/b ÷ c/d)

Method: Invert the second fraction (the divisor) and multiply.

Formula: (a/b) ÷ (c/d) = (a/b) * (d/c) = (ad) / (bc)

Example: 1/2 ÷ 1/3

  1. Invert 1/3 to get 3/1.
  2. Multiply: 1/2 * 3/1
  3. (1*3) / (2*1)
  4. Result: 3/2 (or 1 1/2 as a mixed number)

After calculation, the result is simplified to its lowest terms and can be displayed as a mixed number, improper fraction, or decimal.

Finally, a Fraction Calculator That Makes Sense

I'll be honest, fractions can be a headache. Whether you're a student struggling with homework, a baker doubling a recipe, or a woodworker measuring a project, dealing with numerators and denominators can get confusing. I built this fraction calculator to be the simple, clear tool I wish I always had.

My goal wasn't just to give you an answer, but to help you understand it. That's why my calculator shows the result in three different formats: as a simplified mixed number, as an improper fraction, and as a decimal. This way, you get the answer you need in the format that makes the most sense for your situation.

A Real-World Example: In the Kitchen

Imagine you have a recipe that calls for 1 ¾ cups of flour, but you want to make a half batch. You need to calculate 1 ¾ divided by 2.

You could try to do the math in your head, but it's easy to make a mistake. Instead, let's use my calculator:

  • In "Fraction 1", you'd enter 1 in the whole number box, 3 in the numerator, and 4 in the denominator.
  • Set the operator to "divide" (÷).
  • In "Fraction 2", you'd simply enter 2 in the whole number box.

The calculator instantly gives you the result: . No fuss, no messy conversions. It also tells you the decimal equivalent, 0.875, which can be useful if you're using a kitchen scale.

How I Designed This Fraction Calculator

I wanted this tool to be flexible and intuitive for any kind of fraction problem.

  • Handles All Inputs: You can enter whole numbers, proper fractions, improper fractions, or mixed numbers. Just fill in the boxes you need.
  • All Operations: Easily add, subtract, multiply, and divide.
  • Multiple Results: I show you the answer in its most common forms so you can pick the one you need.
    • Mixed Number: Like 2 ½. Best for everyday understanding.
    • Improper Fraction: Like 5/2. Best for further calculations.
    • Decimal: Like 2.5. Best for measurement.

A Quick Refresher on Fraction Math

You don't need to be a math whiz to use my calculator, but understanding the "why" can be helpful. Here's a quick look at the logic it uses. The first step is always to convert any mixed numbers into improper fractions. For example, 2 ½ becomes 5/2.

Addition and Subtraction (a/b ± c/d)

To add or subtract, fractions need a "common denominator." The calculator finds one, adjusts the numerators, and then performs the operation.

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

Multiplication (a/b * c/d)

This is the easy one! Just multiply the numerators together and the denominators together.

(a/b) * (c/d) = ac / bd

Division (a/b ÷ c/d)

To divide, you "flip" the second fraction (find its reciprocal) and then multiply.

(a/b) ÷ (c/d) = (a/b) * (d/c) = ad / bc

After every calculation, my tool simplifies the resulting fraction to its lowest terms (e.g., 2/4 becomes 1/2) for a clean, final answer.

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