How do I add and subtract fractions?

To add or subtract fractions, first find a common denominator, then add or subtract the numerators while keeping the denominator the same. Simplify the result if possible.

What's the difference between proper and improper fractions?

Proper fractions have numerators smaller than denominators (e.g., 3/4), while improper fractions have numerators equal to or larger than denominators (e.g., 5/4).

How do I convert between fractions and decimals?

To convert fraction to decimal, divide numerator by denominator. To convert decimal to fraction, write the decimal as a fraction with appropriate denominator and simplify.

What is the greatest common divisor (GCD)?

GCD is the largest number that divides both numerator and denominator without remainder. It's used to simplify fractions to their lowest terms.

How do I multiply and divide fractions?

To multiply fractions, multiply numerators and denominators directly. To divide fractions, multiply by the reciprocal (flip the second fraction) of the divisor.

Fraction Calculator

Add, subtract, multiply, and divide fractions instantly with step-by-step solutions. Free fraction calculator for simplifying fractions and converting to decimals. Supports mixed numbers and improper fractions.

Smart Tips

• To add fractions, find a common denominator first, then add the numerators

• Multiplying fractions is straightforward: multiply numerators, multiply denominators

• To divide fractions, multiply by the reciprocal of the divisor (flip and multiply)

• Always simplify your final answer by finding the greatest common factor

• Mixed numbers can be converted to improper fractions before calculating, then converted back

• Reduce fractions before multiplying when possible to keep numbers smaller

Formulas

Operation	Formula
Addition/Subtraction	a/b ± c/d = (ad ± bc) / bd
Multiplication	(a/b) × (c/d) = (a × c) / (b × d)
Division	(a/b) ÷ (c/d) = (a × d) / (b × c)

Key Insights

Common Denominator

When adding or subtracting fractions, find the least common denominator (LCD) to ensure accurate calculations.

Simplification

Always simplify fractions to their lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD).

Multiplication Rules

Multiply numerators together and denominators together. Simplify before multiplying if possible to reduce calculation complexity.

Division Method

To divide fractions, multiply by the reciprocal (flip the second fraction) and then follow multiplication rules.

Frequently Asked Questions

To add or subtract fractions, first find a common denominator (preferably the least common multiple of the denominators), then convert each fraction so it has that denominator, add or subtract the numerators, and keep the denominator the same. Simplify the result by dividing numerator and denominator by their greatest common divisor (GCD) so the fraction is in lowest terms.

Proper fractions have numerators smaller than denominators (e.g., 3/4); they represent values less than 1. Improper fractions have numerators equal to or larger than denominators (e.g., 5/4 or 4/4) and represent values greater than or equal to 1. Improper fractions can be converted to mixed numbers (e.g., 5/4 = 1¼) for easier reading; both forms are mathematically equivalent.

To convert a fraction to a decimal, divide the numerator by the denominator (e.g., 3/4 = 0.75). To convert a decimal to a fraction, write the decimal as a fraction with a power of 10 in the denominator (e.g., 0.75 = 75/100), then simplify to lowest terms (3/4). Repeating decimals require a different approach: set the repeating part as x and solve an equation to get a fraction.

The GCD (greatest common divisor) is the largest positive integer that divides both the numerator and the denominator with no remainder. For example, the GCD of 8 and 12 is 4. It is used to simplify fractions to lowest terms: divide both numerator and denominator by the GCD. The Euclidean algorithm is an efficient way to compute the GCD for any two integers.

To multiply fractions, multiply the numerators together and the denominators together; then simplify (e.g., 2/3 × 4/5 = 8/15). To divide fractions, multiply by the reciprocal of the divisor: flip the second fraction and multiply (e.g., 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6). You can simplify before multiplying to keep numbers smaller—cancel any common factor between a numerator and a denominator.

Our fraction calculations follow standard arithmetic of rational numbers: addition and subtraction via common denominators, multiplication and division by the usual rules, and simplification using the greatest common divisor (GCD) via the Euclidean algorithm. These methods are taught in curricula worldwide and are consistent with definitions used in algebra and number theory.

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Note:Fraction calculations are based on standard mathematical operations. Results are simplified to their lowest terms. For complex fractions, verify calculations manually.