½ Fraction Calculator
Add, subtract, multiply, and divide fractions with step-by-step solutions.
How to Use This Calculator
Enter the numerator and denominator for each fraction, then select the operation you want. The result is shown as a simplified fraction, a mixed number if applicable, and a decimal. The step-by-step breakdown shows exactly how the calculation was done.
Click the operation button: Add (+), Subtract (-), Multiply (×), or Divide (÷).
Enter the numerator (top number) and denominator (bottom number) for Fraction 1.
Enter Fraction 2 the same way. The calculation updates automatically as you type.
Read the result: simplified fraction, mixed number form, the working step, and the decimal equivalent are all shown together.
Fraction Operation Rules
Addition and subtraction need a common denominator. The formula above uses the product b×d as a common denominator, which always works. It may not be the lowest common denominator (LCD), but dividing by the GCD at the end gives the fully simplified result. For multiplication and division, you just multiply or use the reciprocal — no common denominator needed.
Worked Examples
Where This Comes Up in Real Life
Cooking recipes often need fraction arithmetic. If a recipe for 4 people uses 3/4 cup of flour and you want to make it for 6 people, you multiply: 3/4 × 6/4 = 18/16 = 9/8 = 1 and 1/8 cups. Getting this wrong by a significant margin changes the texture of the dish. Baking especially depends on accurate ratios between flour, water, fat, and leavening agents.
Carpenters and engineers work with fractional measurements constantly. Cutting a 7/8 inch piece from a 3/4 inch board requires knowing that 7/8 > 3/4 (which is 6/8) before making any cuts. Structural calculations also involve fractions: a beam spanning 4.5 m with a load at 1/3 of its length requires knowing that 1/3 of 4.5 is 1.5 m. In finance, fractions appear in interest rate calculations and stock price movements quoted in eighths or sixteenths on older exchanges.
Frequently Asked Questions
How do I add fractions with different denominators?
Find the LCM of both denominators (the LCD). Convert each fraction to use the LCD, then add the numerators. Simplify: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
How do I multiply fractions?
Multiply numerators together and denominators together: (a/b) × (c/d) = (a×c)/(b×d). Then simplify. Example: 2/3 × 3/4 = 6/12 = 1/2.
How do I divide fractions?
To divide, multiply by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
What is a mixed number?
A mixed number has a whole part and a fractional part, e.g. 1½. To convert an improper fraction: 7/4 = 1 remainder 3 = 1¾.
How do I simplify a fraction?
Divide both numerator and denominator by their GCD. Example: 12/18 → GCD(12,18)=6 → 12÷6/18÷6 = 2/3.