Fraction Calculator with Step-by-Step Solutions

In our digital world of decimals and percentages, it's easy to think of fractions as a relic of primary school math. Yet, they are everywhere. From a recipe that calls for ¾ cup of flour to a mechanic using a 5/8 inch wrench, or a financial report showing a stock gained ½ a point, fractions provide a precise way to represent parts of a whole. Understanding how to work with them is a fundamental life skill. A fraction calculator is an invaluable tool, not just for getting quick answers, but for learning the logical processes behind the calculations.

Before calculating, let's review the players:

• Numerator: The top number. It tells you how many parts you have.
• Denominator: The bottom number. It tells you how many parts the whole is divided into.
• Proper Fraction: The numerator is smaller than the denominator (e.g., 2/3). It's less than one whole.
• Improper Fraction: The numerator is larger than or equal to the denominator (e.g., 5/3). It's one whole or more.
• Mixed Number: A combination of a whole number and a proper fraction (e.g., 1 ⅔). It's a more intuitive way to write an improper fraction. Our calculator handles all these types seamlessly.

You can't add or subtract fractions unless they're talking about the same-sized pieces. This is the core concept of the Lowest Common Denominator (LCD). You can't add "halves" to "thirds" directly, just like you can't add apples and oranges. You must first convert them to a common unit, "sixths" in this case.

Example: 1/2 + 1/3

1. Find the LCD: The smallest number that both 2 and 3 divide into is 6.
2. Convert the Fractions:
   • To turn 1/2 into sixths, you multiply the denominator by 3, so you must also multiply the numerator by 3: 1/2 becomes 3/6.
   • To turn 1/3 into sixths, you multiply the denominator by 2, so you must also multiply the numerator by 2: 1/3 becomes 2/6.
3. Add the Numerators: Now that the denominators are the same, you just add the numerators: 3/6 + 2/6 = 5/6.

Subtraction follows the exact same process. Our fraction calculator automates the tedious step of finding the LCD and provides a step-by-step breakdown of this conversion.

Multiplying fractions is refreshingly straightforward. There's no need for common denominators. You simply multiply the numerators together and the denominators together.

Example: 2/3 × 3/4

• Multiply numerators: 2 × 3 = 6
• Multiply denominators: 3 × 4 = 12
• Result: 6/12

The final, crucial step is to simplify the result. 6/12 can be reduced to 1/2. A good fraction calculator will always give you the answer in its simplest form.

Dividing by a fraction is the same as multiplying by its reciprocal. This leads to the famous mnemonic: "Keep, Change, Flip."

Example: 1/2 ÷ 1/4

1. Keep: Keep the first fraction the same: 1/2.
2. Change: Change the division sign to multiplication: ×.
3. Flip: Flip the second fraction to find its reciprocal: 1/4 becomes 4/1.
4. Solve: Now you have a simple multiplication problem: 1/2 × 4/1 = 4/2.

Finally, simplify the result. 4/2 simplifies to the whole number 2. The step-by-step solution in our calculator makes this process transparent and easy to follow.

A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. To simplify a fraction like 12/18, you need to find the Greatest Common Divisor (GCD)—the largest number that divides evenly into both numbers.

• The divisors of 12 are 1, 2, 3, 4, 6, 12.
• The divisors of 18 are 1, 2, 3, 6, 9, 18.
• The greatest common divisor is 6.

You then divide both the numerator and the denominator by the GCD:

• 12 ÷ 6 = 2
• 18 ÷ 6 = 3
• So, 12/18 simplifies to 2/3.

This is often the most challenging step to do manually, especially with large numbers. Our fraction calculator uses an efficient algorithm (like the Euclidean algorithm) to find the GCD instantly and guarantee your result is always fully simplified.