Calculator: Completely Reduce (Simplify) Fractions to the Lowest Terms – To the Simplest Equivalent Form, Irreducible, With the Smallest Possible Numerator and Denominator (Prime to Each Other)

Online Calculator: Completely reduce (simplify) fraction to the lowest terms

To fully reduce (simplify) fractions to the lowest terms:

Divide the numerator and denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd).

Result written as a proper or an improper fraction, as a mixed number, as a decimal or an integer and as a percentage.

The latest 10 fractions that have been fully reduced (simplified) to their lowest terms (to their simplest form, the smallest possible numerator and denominator)

Completely reduce (simplify) the fraction 3,165 / 264 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:52 UTC (GMT)
Completely reduce (simplify) the fraction 58,333,333,333 / 100,000,000,000 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:52 UTC (GMT)
Completely reduce (simplify) the fraction 27 / 9 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:52 UTC (GMT)
Completely reduce (simplify) the fraction 4 / 137,577 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:51 UTC (GMT)
Completely reduce (simplify) the fraction 7,319 / 91 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:51 UTC (GMT)
Completely reduce (simplify) the fraction 1,443 / 33,102 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:51 UTC (GMT)
Completely reduce (simplify) the fraction 41,101 / 28,775 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:51 UTC (GMT)
Completely reduce (simplify) the fraction 96 / 44,212 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:51 UTC (GMT)
Completely reduce (simplify) the fraction 6 / 92,042 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:51 UTC (GMT)
Completely reduce (simplify) the fraction 48 / 64 to the lowest terms (to its simplest form, irreducible - the smallest possible numerator and denominator) May 13 01:51 UTC (GMT)
The list of all the fractions that were fully reduced (simplified) to their lowest terms (to their simplest form), the smallest possible numerator and denominator

Tutoring: simplifying fractions - reducing them to the lowest terms

Steps to simplify a fraction, to reduce it to its lowest terms:

  • A fraction fully simplified, a fraction reduced to its lowest terms is a fraction that can no longer be simplified, it has been reduced to its simplest equivalent fraction, the one having the smallest numerator and denominator possible - prime to each other.
  • 1) Run the prime factorization of both the numerator and the denominator of the fraction.
  • 2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.
  • 3) Divide both the numerator and the denominator of the fraction by their greatest common factor, GCF (GCD).
  • The fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
  • A fraction reduced to its lowest terms may no longer be reduced and it is called an irreducible fraction.

Example: reduce the fraction 315/1,155 as much as possible, simplify it to the lowest terms.

  • 1) Run the prime factorization of both the numerator and the denominator of the fraction.

  • The numerator of the fraction is 315, its breaking down into prime factors is:
    315 = 3 × 3 × 5 × 7 = 32 × 5 × 7
  • The denominator of the fraction is 1,155, its breaking down into prime factors is:
    1,155 = 3 × 5 × 7 × 11.

  • 2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.

  • The greatest common factor, gcf (315; 1,155), is calculated by multiplying all the common prime factors of the numerator and the denominator, taken by their lowest powers (their lowest exponents):
  • GCF (315; 1,155) = (32 × 5 × 7; 3 × 5 × 7 × 11) = 3 × 5 × 7 = 105
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  • 3) Divide both the numerator and the denominator of the fraction by their greatest common factor, GCF (GCD).

  • The numerator and denominator of the fraction are divided by their greatest common factor, GCF:
  • 315/1,155 =
    (32 × 5 × 7)/(3 × 5 × 7 × 11) =
    ((32 × 5 × 7) ÷ (3 × 5 × 7)) / ((3 × 5 × 7 × 11) ÷ (3 × 5 × 7)) =
    3/11
  • The fraction thus obtained is called a fraction reduced to the lowest terms.

Why reducing (simplifying) fractions to lower terms?

  • When running operations with fractions we are often required to bring them to the same denominator, for example when adding, subtracting or comparing.
  • Sometimes both the numerators and the denominators of those fractions are large numbers and doing calculations with such numbers could be difficult.
  • By reducing (simplifying) a fraction, both its numerator and denominator are reduced to smaller values, much easier to work with, which will decrease the overall effort of working with that fraction.

Read the entire article ⇒ Completely reduce (simplify) fractions to the lowest terms: Steps and Examples