Fraction Calculator

Step 1: Enter the first fraction. Type the numerator (top number) and denominator (bottom number) in the "Fraction 1" fields.

Step 2: Select the operation: Add (+), Subtract (−), Multiply (×), or Divide (÷).

Step 3: Enter the second fraction in the "Fraction 2" fields.

Step 4: Click Calculate. The result shows the answer as a simplified fraction and its decimal equivalent. The calculator automatically reduces fractions to their lowest terms — for example, 4/8 becomes 1/2.

A fraction represents a part of a whole. It consists of two numbers: the numerator (top) tells how many parts you have, and the denominator (bottom) tells how many equal parts make up the whole. The fraction 3/4 means 3 parts out of 4 equal parts.

Proper fractions have a numerator smaller than the denominator (3/4, 1/2, 5/8). Improper fractions have a numerator equal to or larger than the denominator (5/3, 7/4, 11/8). Mixed numbers combine a whole number and a fraction (1 1/2, 2 3/4). This calculator works with improper fractions but not mixed number notation — convert 2 3/4 to 11/4 before entering.

Equivalent fractions look different but represent the same value. 1/2 = 2/4 = 3/6 = 50/100. You create equivalent fractions by multiplying or dividing both the numerator and denominator by the same number. This calculator always simplifies the result to the lowest equivalent fraction by dividing by the greatest common divisor (GCD).

Why fractions matter: Fractions appear everywhere — cooking recipes (3/4 cup), construction measurements (5/8 inch), music time signatures (3/4 time), probability (1/6 chance), and test scores (42/50). Understanding fraction arithmetic is essential for these everyday applications.

Addition: a/b + c/d = (a×d + c×b) / (b×d)
Find a common denominator by multiplying, then add numerators.
Example: 1/3 + 1/6 = (1×6 + 1×3) / (3×6) = (6+3) / 18 = 9/18 = 1/2

Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
Same process as addition, but subtract numerators.
Example: 3/4 − 1/3 = (3×3 − 1×4) / (4×3) = (9−4) / 12 = 5/12

Multiplication: a/b × c/d = (a×c) / (b×d)
Multiply numerators together and denominators together.
Example: 2/3 × 3/4 = (2×3) / (3×4) = 6/12 = 1/2

Division: a/b ÷ c/d = (a×d) / (b×c)
Flip the second fraction and multiply (multiply by the reciprocal).
Example: 3/4 ÷ 1/2 = (3×2) / (4×1) = 6/4 = 3/2 (or 1.5)

Simplification uses the GCD (Greatest Common Divisor). For 9/18: GCD(9,18) = 9, so 9÷9 / 18÷9 = 1/2.

Example 1: Adding Fractions — Cooking
A recipe calls for 1/3 cup of oil and 1/6 cup of vinegar. How much liquid total? Enter 1/3 + 1/6. Result: 1/2 (0.5 cups). The calculator finds the common denominator (18), adds (6+3=9), and simplifies 9/18 to 1/2.

Example 2: Subtracting Fractions — Materials
You have 7/8 of a yard of fabric and use 1/4. How much remains? Enter 7/8 − 1/4. Result: 5/8 (0.625 yards). The calculation: (7×4 − 1×8) / (8×4) = (28−8)/32 = 20/32 = 5/8.

Example 3: Multiplying Fractions — Probability
The probability of rain is 2/3 and the probability of forgetting an umbrella is 1/4. What is the probability of both? Enter 2/3 × 1/4. Result: 1/6 (0.1667 or about 16.7% chance).

Convert mixed numbers before entering. This calculator accepts improper fractions, not mixed numbers. To convert: multiply the whole number by the denominator, add the numerator. Example: 2 3/4 = (2×4+3)/4 = 11/4.

The result is always simplified. You do not need to reduce the answer yourself. The calculator finds the greatest common divisor and divides both parts automatically.

Negative fractions work. Enter a negative numerator to represent a negative fraction. For example, -3/4 is entered as numerator = -3, denominator = 4.

Denominators cannot be zero. Division by zero is undefined in mathematics. If you enter 0 as a denominator, the calculator will show an error.

Use division to find "how many times." How many 1/4-cup scoops fit in 3/4 cup? Enter 3/4 ÷ 1/4 = 3. Exactly 3 scoops.