Simplify Fractions Calculator

Simplify Fractions is evaluated from Numerator and Denominator. The calculation reports Simplified Fraction, Mixed Number and GCD Used.

Results

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About the Simplify Fractions Calculator

Simplify Fractions is treated here as a quantitative relation between Numerator and Denominator and Simplified Fraction, Mixed Number, GCD Used and Decimal Value.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
_num = parseInt(numerator)
_den = parseInt(denominator)
_gcd = (function gcd(a,b){a=Math.abs(a);b=Math.abs(b);while(b){var t=b;b=a%b;a=t;}return a;})(_num,_den)
gcd_val = _gcd
_sNum = _num / _gcd
_sDen = _den / _gcd
_sign = (_num < 0) !== (_den < 0) ? '-': ''
_aN = Math.abs(_sNum)
_aD = Math.abs(_sDen)
simplified = _sign + _aN + '/' + _aD
_whole = Math.floor(_aN / _aD)
_rem = _aN% _aD
mixed_number = _aN >= _aD ? (_rem === 0 ? '' + _sign + _whole: _sign + _whole + ' ' + _rem + '/' + _aD): simplified
decimal_val = _num / _den

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

_num = parseInt(numerator)
_den = parseInt(denominator)
_gcd = (function gcd(a,b){a=Math.abs(a);b=Math.abs(b);while(b){var t=b;b=a%b;a=t;}return a;})(_num,_den)
gcd_val = _gcd
_sNum = _num / _gcd
_sDen = _den / _gcd
_sign = (_num < 0) !== (_den < 0) ? '-': ''
_aN = Math.abs(_sNum)
_aD = Math.abs(_sDen)
simplified = _sign + _aN + '/' + _aD
_whole = Math.floor(_aN / _aD)
_rem = _aN% _aD
mixed_number = _aN >= _aD ? (_rem === 0 ? '' + _sign + _whole: _sign + _whole + ' ' + _rem + '/' + _aD): simplified
decimal_val = _num / _den

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Simplify 18/24

Inputs

numerator: 18 denominator: 24
Simplified Fraction: 3/4. Mixed Number: 3/4. GCD Used: 6. Decimal Value: 0.75

With Numerator = 18 and Denominator = 24 as the stated inputs, the result is Simplified Fraction = 3/4, Mixed Number = 3/4 and GCD Used = 6. Each value corresponds to the declared output fields.

Example 2: Simplify improper fraction 45/18

Inputs

numerator: 45 denominator: 18
Simplified Fraction: 5/2. Mixed Number: 2 1/2. GCD Used: 9. Decimal Value: 2.5

With Numerator = 45 and Denominator = 18 as the stated inputs, the result is Simplified Fraction = 5/2, Mixed Number = 2 1/2 and GCD Used = 9. Each value corresponds to the declared output fields.

Example 3: Simplify 100/1000

Inputs

numerator: 100 denominator: 1000
Simplified Fraction: 1/10. Mixed Number: 1/10. GCD Used: 100. Decimal Value: 0.1

With Numerator = 100 and Denominator = 1,000 as the stated inputs, the result is Simplified Fraction = 1/10, Mixed Number = 1/10 and GCD Used = 100. Each value corresponds to the declared output fields.

Example 4: Negative fraction: simplify -36/48

Inputs

numerator: -36 denominator: 48
Simplified Fraction: -3/4. Mixed Number: -3/4. GCD Used: 12. Decimal Value: -0.75

With Numerator = -36 and Denominator = 48 as the stated inputs, the result is Simplified Fraction = -3/4, Mixed Number = -3/4 and GCD Used = 12. Each value corresponds to the declared output fields.

Common Use Cases

  • Simplify a fraction to lowest terms
  • Find the GCD of numerator and denominator
  • Convert improper fractions to mixed numbers