Fraction Calculator
Step-by-Step Solution
How to Calculate with Fractions
Fractions represent parts of a whole, written as a numerator over a denominator. Working with fractions is a foundational math skill used in cooking, construction, engineering, and everyday problem-solving. This calculator performs all four basic operations on fractions and shows you exactly how each answer is reached.
For addition and subtraction, fractions must share a common denominator. The calculator finds the least common denominator (LCD) automatically, converts each fraction, then adds or subtracts the numerators. For multiplication, the process is simpler: multiply numerators together and denominators together. Division is handled by multiplying the first fraction by the reciprocal (flipped version) of the second.
Every result is automatically simplified to its lowest terms using the greatest common divisor (GCD). The GCD is found using the Euclidean algorithm, which repeatedly divides the larger number by the smaller until the remainder is zero. Both the simplified fraction and its decimal equivalent are displayed. The step-by-step breakdown helps students understand the process rather than just memorizing rules, making this tool ideal for homework help and learning reinforcement.
Formula
Addition/Subtraction:
a/b ± c/d = (a×d ± c×b) / (b×d)
Multiplication:
a/b × c/d = (a×c) / (b×d)
Division:
a/b ÷ c/d = (a×d) / (b×c)
Where:
- a, c = numerators
- b, d = denominators (cannot be zero)
- Results are simplified using the greatest common divisor (GCD)
Example Calculation
Scenario: Add 2/3 + 3/4
- Step 1: Find LCD of 3 and 4 = 12
- Step 2: Convert: 2/3 = 8/12, 3/4 = 9/12
- Step 3: Add numerators: 8 + 9 = 17
- Result: 17/12 = 1 5/12 (approximately 1.4167)