Simplify Fractions Calculator
By Hesaplayıcı
The fraction simplifier reduces the fraction you enter to lowest terms. Enter the numerator and the denominator; the calculator divides both by their greatest common divisor (GCD). Next to the simplified fraction it shows the GCD, the decimal value and, for an improper fraction, the mixed number. A negative denominator moves its sign to the numerator.
Worked example: Simplify 84/126
Decimal value
0.67
- Simplified numerator
- 2
- Simplified denominator
- 3
- GCD (greatest common divisor)
- 42
- Whole part
- 0
- Remainder (numerator of the mixed number)
- 2
Step by step
GCD (greatest common divisor)
GCD = gcd(|numerator|, denominator)
GCD = gcd(84, 126) = 42
Simplified numerator
simplified numerator = numerator / GCD
simplified numerator = 84 / 42 = 2
Simplified denominator
simplified denominator = denominator / GCD
simplified denominator = 126 / 42 = 3
Decimal value
decimal = numerator / denominator
decimal = 84 / 126 = 0.67
Whole part
whole part = (simplified numerator − remainder) / simplified denominator
whole part = (2 − 2) / 3 = 0
Remainder (numerator of the mixed number)
remainder = simplified numerator − whole part × simplified denominator
remainder = 2 − 0 × 3 = 2
How to use
- Enter the Numerator as a whole number. It can be negative.
- Enter the Denominator as a whole number. It cannot be zero.
- Press Calculate. You get the simplified fraction, the GCD, the decimal value, the whole part and the remainder.
Formula
GCD = gcd(|numerator|, denominator)simplified numerator = numerator / GCDandsimplified denominator = denominator / GCDdecimal = numerator / denominatorremainder = simplified numerator − whole part × simplified denominator
The GCD is the largest whole number that divides both the numerator and the denominator; the calculator finds it with Euclid’s algorithm. The whole part is the whole-number part of the simplified numerator divided by the simplified denominator. Read the mixed number as whole part + remainder / simplified denominator. A negative denominator is first moved with the rule a / −b = −a / b.
Worked example
The worked example on this page simplifies 84/126. The steps give the GCD first, then the simplified numerator and denominator, and last the decimal value, the whole part and the remainder.
Limits
The calculator simplifies one fraction of whole numbers; it does not add, subtract, multiply or divide fractions. For a negative fraction, the whole part and the remainder are both negative. The decimal is not rounded; the page may shorten it. The numerator and the denominator can be at most 10¹².
Frequently Asked Questions
How do you simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor (GCD). For example, the GCD of 10 and 15 is 5, so 10/15 simplifies to 2/3.
How do you turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator over the same denominator. For example, 11/6 = 1 5/6.
What happens to a negative denominator?
Since a / −b = −a / b, the minus sign moves to the numerator. The simplified denominator is always positive.
Can the denominator be zero?
No. Division by zero is undefined, so the calculator returns an error for a zero denominator.
Calculation rules
- The fraction is simplified by dividing the numerator and the denominator by their GCD. The simplified denominator is always positive; a minus sign moves to the numerator, since a / −b = −a / b.
- Mixed number: whole part + remainder / simplified denominator. For a negative fraction both are negative: −7/3 = −2 and −1/3, that is −2 1/3.
- The denominator cannot be zero. A zero numerator gives 0/1.
- The decimal is not rounded; the page may shorten numbers.