Simplify Fractions Calculator
Enter a numerator and a denominator to reduce the fraction to simplest form. Improper fractions are also shown as mixed numbers.
Result
- As a mixed number
- 3/4
- As a decimal
- 0.75
- Greatest common factor
- 14
- Working
- 42 ÷ 14 = 3 and 56 ÷ 14 = 4
- Equivalent fractions
- 6/8, 9/12, 12/16, 15/20
Formula
- Simplified fraction = (numerator ÷ GCF) / (denominator ÷ GCF)
- Mixed number: whole part = numerator ÷ denominator, fraction = remainder / denominator
How the Simplify Fractions Calculator works
A fraction is in simplest form when the numerator and denominator have no common factor except 1. Dividing both by their greatest common factor gets there in one step.
Simplifying does not change the value. 42/56 and 3/4 name the same number, because multiplying or dividing the top and bottom by the same amount is the same as multiplying by 1.
Worked example
For 42/56 the greatest common factor is 14. 42 ÷ 14 = 3 and 56 ÷ 14 = 4, so the fraction simplifies to 3/4, or 0.75.
Frequently asked questions
How do I know if a fraction is fully simplified?
The numerator and denominator share no factor other than 1. Check by finding their greatest common factor: if it is 1, the fraction is in lowest terms.
What are equivalent fractions?
Fractions with the same value written with different numbers. 1/2, 2/4 and 5/10 are equivalent.
Related calculators
- Fraction CalculatorAdd, subtract, multiply and divide fractions and mixed numbers. The answer is simplified and shown as a fraction, a mixed number and a decimal.
- GCF Calculator (Greatest Common Factor)Find the greatest common factor of two or more numbers, with the Euclidean algorithm steps and prime factorizations. Also gives the LCM.
- Decimal to Fraction CalculatorConvert a decimal to a fraction in lowest terms, or a fraction to a decimal. Exact conversion for terminating decimals.
- Ratio CalculatorSimplify a ratio, solve for a missing value in A : B = C : D, or split a total in a given ratio. Works with whole numbers and decimals.
- Proportion CalculatorSolve a proportion a/b = c/d for the missing value by cross-multiplication. Enter any three of the four numbers.
- Factor CalculatorFind all factors of a number, its factor pairs and its prime factorization. Also tells you whether the number is prime.
- LCM Calculator (Least Common Multiple)Find the least common multiple of two or more numbers, with prime factorizations. Also gives the greatest common factor.
- Rounding CalculatorRound a number to the nearest whole number, tenth, hundredth, thousandth, ten, hundred or thousand. Exact decimal rounding with no floating point errors.
- Significant Figures CalculatorCount the significant figures in a number and round it to any number of significant figures, with scientific notation.
- Modulo CalculatorCalculate a mod n, the remainder after division, with the quotient. Handles negative numbers under both the mathematical and programming conventions.
- Long Division CalculatorDivide whole numbers and see every step of the long division, with the quotient, remainder, mixed number and decimal answer.
Related unit converters
Calculations run in your browser and nothing you enter is sent to a server. Results are provided for general information. Check critical figures independently before relying on them.