Fraction Calculator

Add, subtract, multiply, and divide fractions. See simplified results and step-by-step solutions.

/
/

Result (Fraction)

—

Decimal Equivalent

—

Step-by-Step Solution

—

How Fractions Work

Parts of a Fraction

A fraction has two parts: the numerator (top number, representing parts you have) and the denominator (bottom number, representing total equal parts).

Addition & Subtraction

You need a common denominator to add or subtract fractions. Multiply each fraction so they share the same bottom number, then add or subtract the top numbers.

Multiplication

Multiply numerators together and denominators together. This is the simplest fraction operation: a/b × c/d = (a×c) / (b×d).

Division

Flip the second fraction (take its reciprocal) and multiply: a/b ÷ c/d = a/b × d/c.

Simplifying Fractions

Find the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divide both by it. For example:

  • 12/18: GCD(12, 18) = 6 → 2/3
  • 8/20: GCD(8, 20) = 4 → 2/5
  • 15/25: GCD(15, 25) = 5 → 3/5

Converting to Decimals

Divide the numerator by the denominator. Some fractions give exact decimals (1/4 = 0.25), while others repeat (1/3 = 0.333...).

Frequently Asked Questions

How do you add fractions with different denominators?
To add fractions with different denominators, first find a common denominator by multiplying the two denominators together (or finding the least common multiple). Then convert each fraction so they share that denominator, add the numerators, and simplify the result. For example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
How do you simplify a fraction?
To simplify (or reduce) a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, 8/12: the GCD of 8 and 12 is 4, so 8/12 = (8÷4)/(12÷4) = 2/3.
What is the difference between fractions and decimals?
Fractions represent a part of a whole as a ratio of two integers (like 3/4), while decimals represent the same value using place values after a decimal point (like 0.75). To convert a fraction to a decimal, divide the numerator by the denominator. Some fractions produce repeating decimals (like 1/3 = 0.333...).
How do you multiply and divide fractions?
To multiply fractions, multiply the numerators together and the denominators together, then simplify. For example, 2/3 × 3/4 = 6/12 = 1/2. To divide fractions, flip the second fraction (reciprocal) and multiply. For example, 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.

Related Calculators

📊
Math

Percentage Calculator

Calculate percentages, percentage change, and percentage of a number instantly.

📉
Math

Average Calculator

Calculate mean, median, mode, and range for any set of numbers.

√
Math

Square Root Calculator

Find square roots, cube roots, and nth roots of any number with decimal precision.

🧮
Math

GCD & LCM Calculator

Find the greatest common divisor and least common multiple of two or more numbers.

💰
Finance

Loan Calculator

Calculate monthly payments, total interest, and amortization schedule for any loan type.

🏠
Finance

Mortgage Calculator

Estimate monthly mortgage payments including principal, interest, taxes, and insurance.