Fraction Calculator

Our comprehensive Fraction Calculator allows you to easily add, subtract, multiply, and divide fractions. You can also simplify fractions to their lowest terms, convert between fractions and decimals, and work with mixed numbers. Get instant results in both fractional and decimal form. Ideal for students, teachers, chefs, and anyone working with fractions.

Tips

Denominators cannot be zero.
Results are automatically simplified to lowest terms.

Calculate Fractions

Enter values and select an operation to perform a calculation.

About This Calculator

A fraction represents a part of a whole. It consists of two numbers: a numerator (the number above the line) and a denominator (the number below the line). For example, in the fraction $\frac{3}{4}$ , 3 is the numerator and 4 is the denominator.

This calculator allows you to perform basic arithmetic operations with fractions: addition, subtraction, multiplication, division, simplification, and comparison. Simply enter your fractions, select an operation, and click Calculate to see the result in both fraction and decimal form.

How to Use

Using the Fraction Calculator is straightforward:

Choose whether to use mixed numbers: Toggle the "Use Mixed Numbers" checkbox if you want to work with mixed numbers like 1 3/4.
Enter the first fraction: Input the numerator and denominator in the respective fields. If using mixed numbers, also enter the whole number part.
Select an operation: Choose from add, subtract, multiply, divide, simplify, or compare.
- For the "Simplify" operation, only the first fraction is used.
- For the "Compare" operation, the calculator will determine which fraction is larger.
Enter the second fraction: Input the numerator and denominator for the second fraction (if needed for the selected operation).
Click Calculate: The result will be displayed with various visualizations and explanations.

Interpreting Results

The calculator displays results in multiple formats:

Fraction: The simplified result in the form of a fraction (e.g., 3/4).
Mixed Number: For improper fractions (where the numerator is greater than the denominator), the result is shown as a mixed number (e.g., 1 1/4).
Decimal: The equivalent decimal value (e.g., 0.75).
Percentage: The equivalent percentage value (e.g., 75%).
Step-by-Step Solution: A detailed explanation of how the result was calculated, including the mathematical formulas used at each step.
Visual Representation: Charts that help visualize the fractions and their relationships.
Comparison Result: When using the compare operation, the calculator shows which fraction is greater, less than, or equal to the other.

All fractions are automatically simplified to their lowest terms. For example, if a calculation results in $\frac{4}{8}$ , it will be simplified to $\frac{1}{2}$ .

Methodology

The calculator uses standard arithmetic rules for fraction operations:

Mixed Numbers and Improper Fractions

A mixed number consists of a whole number and a proper fraction. For example, 2 3/4.

To convert a mixed number to an improper fraction:

a \frac{b}{c} = \frac{a \times c + b}{c}

For example, 2 3/4 = (2 × 4 + 3)/4 = 11/4

Addition

To add fractions with the same denominator:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

To add fractions with different denominators:

\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

Subtraction

Similar to addition, but we subtract the numerators:

\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}

Multiplication

Multiply the numerators and the denominators:

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Division

To divide fractions, multiply by the reciprocal of the second fraction:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}

Simplification

To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).

\frac{a}{b} = \frac{a \div \text{gcd}(a,b)}{b \div \text{gcd}(a,b)}

Comparison

To compare two fractions, we can convert them to a common denominator or use cross multiplication:

\frac{a}{b} \text{ compared to } \frac{c}{d}

a \times d \text{ compared to } b \times c

If a×d > b×c, then a/b > c/d

If a×d < b×c, then a/b < c/d

If a×d = b×c, then a/b = c/d

Applications

Fractions are used in many real-world scenarios:

Cooking and baking (e.g., 3/4 cup of flour)
Construction and woodworking (e.g., 5/8 inch measurement)
Finance and probability
Academic contexts in mathematics, physics, and engineering
Music notation (e.g., 3/4 time signature)
Medicine for dosage calculations

Frequently Asked Questions

Q: What if a denominator is zero?

A: Division by zero is undefined in mathematics. The calculator will show an error message if you try to use a zero denominator or perform a calculation that results in a zero denominator.

Q: Can I enter negative fractions?

A: Yes, you can input negative numbers for either the numerator or denominator. The calculator handles negative fractions correctly in all operations.

Q: What is a mixed number?

A: A mixed number consists of a whole number and a proper fraction, such as 3 1/2 (three and a half). The calculator can handle both mixed numbers and improper fractions.

Q: How are fractions simplified?

A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator, then divides both by this number to reduce the fraction to its lowest terms.

Q: Why do I need step-by-step explanations?

A: Step-by-step explanations help in understanding the mathematical process and are particularly useful for educational purposes or to verify that calculations are correct.