Fraction Calculator: Add, Simplify & Decimals

Calculated using standard mathematical and industry formulas.

To solve fractions, find the least common denominator (LCD) for addition and subtraction, multiply numerators and denominators directly for multiplication, and multiply by the reciprocal for division. Always simplify results to lowest terms by dividing by the greatest common divisor (GCD). This tool provides step-by-step solutions and instant decimal conversions.

How to use this calculator?

  1. Select the operation: Addition (+), Subtraction (-), Multiplication (×), or Division (÷).
  2. Enter the numerator and denominator for the first fraction.
  3. Enter the numerator and denominator for the second fraction.
  4. Read your answer as a simplified fraction, mixed number, and decimal value.

Formula & calculation method

Standard Fraction Arithmetic Rules

Addition: (a/b) + (c/d) = (a·d + b·c) / (b·d); Division: (a/b) ÷ (c/d) = (a·d) / (b·c); Simplification: a/b = (a ÷ GCD(a,b)) / (b ÷ GCD(a,b)); Decimal = a ÷ b

a, c = numerators; b, d = denominators (b, d ≠ 0). Results are simplified using GCD(num, den).

Step-by-step calculation example

1/2 + 1/4 = (1×4 + 1×2) / (2×4) = 6/8 = 3/4 (0.75).

Key insights to remember

How to interpret your results?

Proper, Improper, and Mixed Fractions

A proper fraction has a numerator smaller than its denominator (e.g., 3/4). An improper fraction has a larger numerator (e.g., 7/4), which converts into a mixed number (1 3/4 or 1.75 in decimal form).

Finding the Least Common Denominator (LCD)

The LCD is the lowest common multiple (LCM) of denominators, allowing fractions with different parts to be combined without inflating calculation numbers.

Expert advice & guidance

💡 Math study tip: When converting fractions to decimals, memorizing common benchmark equivalents (1/8 = 0.125, 1/4 = 0.25, 1/3 = 0.333..., 1/2 = 0.5, 3/4 = 0.75) saves significant time on standardized tests and technical blueprints.

Frequently asked questions

How to simplify fractions and reduce to lowest terms?
To simplify a fraction to lowest terms: find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both numbers by that factor. For example, to simplify 12/16, the GCD is 4: (12 ÷ 4) / (16 ÷ 4) = 3/4.
How to convert decimals to fractions and turn decimals into fractions?
To convert a decimal to a fraction: write the decimal digits over a power of 10 matching the number of decimal places (e.g., 0.75 has two places, so 75/100). Then reduce to lowest terms by dividing numerator and denominator by their GCD (75/100 = 3/4).
How to convert fractions to decimals and turn a fraction into a decimal?
To convert a fraction to a decimal, divide the top numerator by the bottom denominator using long division or a calculator. For example, 3/4 is 3 ÷ 4 = 0.75, and 1/3 is 1 ÷ 3 = 0.3333... (a repeating recurring decimal).
How to find the least common denominator (LCD) and what is a common denominator?
The Least Common Denominator (LCD) is the smallest positive integer that is evenly divisible by all denominators in a problem. To find it, list the multiples of each denominator or find their Least Common Multiple (LCM). For 1/4 and 1/6, the LCD is 12.
What are common fraction to decimal equivalents (1/3, 3/4, 3/8, 1/8, 2/5)?
Essential fraction-to-decimal benchmarks: 1/2 = 0.5, 1/3 = 0.333..., 2/3 = 0.666..., 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 2/5 = 0.4, 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, and 7/8 = 0.875.

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