Fraction Calculator

1. Select the operation. Choose addition (+), subtraction (-), multiplication (×), or division (÷) from the buttons at the top.
2. Enter the first fraction. Use the numerator and denominator fields. For mixed numbers (like 2 and 3/4), enter 2 in the whole field and 3/4 in the fraction fields. Leave the whole field empty for proper fractions.
3. Enter the second fraction in the same format.
4. Read the results. The answer appears as a simplified fraction (reduced to lowest terms), as a mixed number if applicable, and as a decimal equivalent. The step-by-step work shows exactly how the calculation was done, useful for checking homework or understanding the process.

The calculator handles negative fractions and fractions with large numerators and denominators. For improper fractions where the numerator is larger than the denominator (like 7/4), the result is also shown as a mixed number (1 and 3/4).

Each fraction operation follows a specific method. The key rules:

Addition and Subtraction (need common denominator):
a/b + c/d = (a×d + c×b) / (b×d), then simplify
Example: 2/3 + 1/4 = (8 + 3) / 12 = 11/12

Multiplication (no common denominator needed):
a/b × c/d = (a×c) / (b×d), then simplify
Example: 2/3 × 3/5 = 6/15 = 2/5

Division (multiply by the reciprocal):
a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Example: 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 and 1/8

Simplifying (reduce to lowest terms):
Divide numerator and denominator by their GCF
Example: 12/18, GCF = 6, so 12/6 = 2, 18/6 = 3, result = 2/3

Finding the Least Common Denominator (LCD) for addition and subtraction: if the denominators share no common factors (like 3 and 4), multiply them together (LCD = 12). If they share factors (like 4 and 6, which share a factor of 2), the LCD is 12 (not 24). The LCD is the Least Common Multiple of both denominators.