Fraction Calculator
Add, subtract, multiply, divide, and simplify fractions, or convert mixed numbers with exact integer arithmetic.
Calculate the exact sum of two fractions (a/b + c/d) using common denominators and reduction.
Addition Result
How Fractions Are Calculated
Exact mathematical formulas for fraction arithmetic, reduction via GCD, and mixed number conversions.
1. Fraction Addition Formula
To add two fractions, find a common denominator (ideally the Least Common Multiple of b and d), scale both numerators accordingly, add them together, and simplify by their GCD.
When to use: Use when combining fractional quantities, ingredients, or parts of a whole.
2. Fraction Subtraction Formula
To subtract fractions, find a common denominator, scale both numerators, subtract the second numerator from the first, and reduce the result to lowest terms.
When to use: Use when finding the difference between two fractional amounts.
3. Fraction Multiplication Formula
To multiply fractions, multiply the numerators together and the denominators together. You can cross-cancel common factors before multiplying to keep numbers small.
When to use: Use when finding a fraction of another fraction or scaling measurements.
4. Fraction Division Formula (Reciprocal)
Dividing by a fraction is equivalent to multiplying by its reciprocal (flipping the numerator and denominator of the divisor).
When to use: Use when dividing quantities into fractional portions or determining ratios.
5. Fraction Simplification (GCD Reduction)
A fraction is in simplest form when its numerator and denominator share no common positive divisor other than 1. Dividing both by their Greatest Common Divisor reduces the fraction.
When to use: Use to express any fraction in standard, lowest irreducible terms.
6. Mixed Number Conversion Formula
To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.
When to use: Use when preparing mixed numbers for mathematical operations or converting improper fractions back to readable quantities.
Practical Calculation Examples
Real-world scenarios illustrating step-by-step numbers, inputs, and verified outputs.
Example 1: Add Fractions 1/2 + 1/3
Find the exact sum of 1/2 and 1/3.
Example 2: Subtract Fractions 3/4 - 1/6
Find the exact difference between 3/4 and 1/6.
Example 3: Multiply Fractions 2/3 × 3/5
Multiply 2/3 by 3/5 and simplify.
Example 4: Divide Fractions 2/3 ÷ 4/5
Divide 2/3 by 4/5 using reciprocal multiplication.
Example 5: Simplify Fraction 18/24
Reduce 18/24 to lowest terms using GCD.
Example 6: Convert Mixed Number 2 1/3 to Improper
Convert mixed number 2 1/3 to improper fraction 7/3.
Frequently Asked Questions
Clear answers to common questions about fraction arithmetic, lowest terms, LCD, and mixed numbers.
How do I use a fraction in a calculator?
To use a fraction in this calculator, select your desired operation (Add, Subtract, Multiply, Divide, Simplify, or Mixed Number), enter the integer numerators and denominators into their dedicated fields, and the calculator will instantaneously generate the exact reduced fraction, step-by-step work, and decimal approximation.
How do I solve fractions on a calculator?
Choose the operation mode matching your problem, enter the numerators and non-zero denominators, and the solver executes exact integer arithmetic. It automatically identifies common denominators, performs reciprocal multiplication for division, and reduces the answer to lowest terms using GCD.
How do I simplify a fraction?
Use the 'Simplify Fraction' mode to enter your numerator and denominator. The calculator determines the Greatest Common Divisor (GCD) of both numbers using the Euclidean algorithm and divides both by it to produce the irreducible lowest form (e.g., 18/24 simplifies to 3/4).
How do I convert a fraction to a decimal?
To convert a fraction to a decimal, divide the top numerator by the bottom denominator (e.g., 3 ÷ 4 = 0.75). In YourCalculate, every fraction calculation automatically provides a precise decimal approximation in the secondary result metrics.
How do you add fractions with different denominators?
To add fractions with different denominators, first find the Least Common Denominator (LCD). Multiply the numerator and denominator of each fraction so they share this common denominator, then add the numerators together while keeping the denominator the same, reducing by GCD.
How do you divide fractions using the reciprocal?
To divide by a fraction, invert the divisor (flip the second fraction to obtain its reciprocal) and multiply: a/b ÷ c/d = a/b × d/c = ad/bc. Dividing by a fraction equal to zero is mathematically undefined.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, for 2 1/3: (2 × 3 + 1) / 3 = 7/3.
What is the difference between a proper and improper fraction?
A proper fraction has a numerator that is smaller than its denominator (e.g., 3/4), representing a value less than 1. An improper fraction has a numerator equal to or greater than its denominator (e.g., 7/3 or 5/5), representing a value of 1 or greater.
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