Free Online Fraction Calculator with Steps
Easily add, subtract, multiply, and divide fractions with our free, step-by-step tool. Get instant answers in simplest form and decimal format.
Solve Any Fraction Problem
How to Use the Fraction Calculator
Our calculator is designed for ease of use, whether you are working with simple fractions, mixed numbers, or whole numbers. Here’s how to get your answer in four simple steps:
- Enter Your First Fraction: In the first group of boxes on the left, enter your fraction. If it's a mixed number like 1 ½, type `1` in the "Whole" box, `1` in the "Numerator" box, and `2` in the "Denominator" box. For a simple fraction like ¾, leave the "Whole" box empty.
- Choose an Operation: Click on one of the four operator buttons (+, −, ×, ÷) to select the calculation you want to perform. The active operator will be highlighted.
- Enter Your Second Fraction: In the second group of boxes on the right, enter your second fraction or mixed number, just as you did in the first step.
- Calculate: Click the "Calculate" button. The tool will instantly display the result in both its simplest fractional form and as a decimal, along with a detailed breakdown of the steps taken to reach the solution.
A Complete Guide to Understanding Fractions
A fraction is a fundamental concept in mathematics that represents a part of a whole. It's a way of expressing a number that isn't a whole number. Every fraction has two main components:
[Image of a pie chart showing a fraction]The Numerator and the Denominator
- Numerator (the top number): This tells you how many parts of the whole you have. For example, in the fraction ¾, the numerator is 3.
- Denominator (the bottom number): This tells you how many equal parts the whole has been divided into. In ¾, the denominator is 4. This means the whole is divided into 4 equal parts, and we are considering 3 of them.
Types of Fractions
Fractions can be categorized into several types, which our **Fraction Calculator** handles seamlessly:
- Proper Fractions: The numerator is smaller than the denominator (e.g., ½, ⅚). These fractions are always less than 1.
- Improper Fractions: The numerator is greater than or equal to the denominator (e.g., ⁵/₄, ⁷/₃). These fractions are always 1 or greater.
- Mixed Numbers (or Mixed Fractions): A combination of a whole number and a proper fraction (e.g., 1 ½, 3 ¾). They represent the same value as an improper fraction. For example, 1 ½ is the same as ³/₂.
How to Manually Calculate Fraction Operations
Understanding the process behind the calculations is key to mastering fractions. Here’s a breakdown of how to perform the four basic operations manually.
Adding and Subtracting Fractions
To add or subtract fractions, they must have a **common denominator**. If they don't, you need to find one.
- Find a Common Denominator: Find the Least Common Multiple (LCM) of the two denominators. For example, to add ½ and ⅓, the LCM of 2 and 3 is 6.
- Convert the Fractions: Rewrite each fraction as an equivalent fraction with the new common denominator. (½ becomes ³/₆, and ⅓ becomes ²/₆).
- Add or Subtract the Numerators: Add (or subtract) the top numbers and keep the denominator the same. (³ + ²)/₆ = ⁵/₆.
- Simplify: If necessary, simplify the resulting fraction to its lowest terms.
Multiplying Fractions
Multiplication is the most straightforward fraction operation.
- Multiply the Numerators: Multiply the top numbers of the two fractions together.
- Multiply the Denominators: Multiply the bottom numbers of the two fractions together.
- Simplify: Reduce the resulting fraction to its lowest terms. For example, ½ × ¾ = (1×3)/(2×4) = ³/₈.
Dividing Fractions
To divide fractions, you "invert and multiply."
- Invert the Second Fraction: Flip the second fraction by swapping its numerator and denominator. This is called finding the reciprocal. (Dividing by ¾ becomes multiplying by ⁴/₃).
- Multiply: Change the division sign to a multiplication sign and multiply the first fraction by the inverted second fraction. For example, ½ ÷ ¾ becomes ½ × ⁴/₃.
- Calculate and Simplify: Multiply the numerators and denominators as before. ½ × ⁴/₃ = ⁴/₆, which simplifies to ²/₃.
What Does it Mean to Simplify Fractions?
Simplifying a fraction (or reducing it to its lowest terms) means to make the numerator and denominator as small as possible while keeping the value of the fraction the same. This is done by dividing both the top and bottom numbers by their **Greatest Common Divisor (GCD)**.
The GCD is the largest number that divides into both the numerator and the denominator without leaving a remainder. For example, consider the fraction ¹²/₁₈:
- The numbers that divide 12 are 1, 2, 3, 4, 6, 12.
- The numbers that divide 18 are 1, 2, 3, 6, 9, 18.
The greatest number they have in common is 6. Therefore, the GCD is 6. To simplify, we divide both parts by 6:
12 ÷ 6 = 2 (new numerator)
18 ÷ 6 = 3 (new denominator)
So, ¹²/₁₈ simplified is ²/₃. Our **Fraction Calculator** performs this simplification automatically for every answer.