Ordinary math fractions reducing to lowest terms (simplifying)

Online calculator: reduce (simplify) fractions

How to reduce (simplify) to the lowest terms ordinary math fraction:

To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

Result written as a proper or improper fraction, a mixed number or a decimal

see more: Coprime numbers (relatively prime)


Latest reduced (simplified) fractions

55/6 already reduced (simplified) to lowest terms
55 > 6 => improper fraction

Rewrite:
55 ÷ 6 = 9 and remainder = 1 =>
55/6 = (9 × 6 + 1)/6 = 9 + 1/6 =
= 9 1/6, mixed number (mixed fraction)
Sep 24 10:29 UTC (GMT)
54/108 = (54 ÷ 54)/(108 ÷ 54) = 1/2 Sep 24 10:29 UTC (GMT)
60/72 = (60 ÷ 12)/(72 ÷ 12) = 5/6 Sep 24 10:29 UTC (GMT)
150/234 = (150 ÷ 6)/(234 ÷ 6) = 25/39 Sep 24 10:29 UTC (GMT)
40/550 = (40 ÷ 10)/(550 ÷ 10) = 4/55 Sep 24 10:29 UTC (GMT)
45/32 already reduced (simplified) to lowest terms
45 > 32 => improper fraction

Rewrite:
45 ÷ 32 = 1 and remainder = 13 =>
45/32 = (1 × 32 + 13)/32 = 1 + 13/32 =
= 1 13/32, mixed number (mixed fraction)
Sep 24 10:29 UTC (GMT)
753/752 already reduced (simplified) to lowest terms
753 > 752 => improper fraction

Rewrite:
753 ÷ 752 = 1 and remainder = 1 =>
753/752 = (1 × 752 + 1)/752 = 1 + 1/752 =
= 1 1/752, mixed number (mixed fraction)
Sep 24 10:29 UTC (GMT)
255/180 = (255 ÷ 15)/(180 ÷ 15) = 17/12;
17 > 12 => improper fraction

Rewrite:
17 ÷ 12 = 1 and remainder = 5 =>
17/12 = (1 × 12 + 5)/12 = 1 + 5/12 =
= 1 5/12, mixed number (mixed fraction)
Sep 24 10:29 UTC (GMT)
26/40 = (26 ÷ 2)/(40 ÷ 2) = 13/20 Sep 24 10:29 UTC (GMT)
67/32 already reduced (simplified) to lowest terms
67 > 32 => improper fraction

Rewrite:
67 ÷ 32 = 2 and remainder = 3 =>
67/32 = (2 × 32 + 3)/32 = 2 + 3/32 =
= 2 3/32, mixed number (mixed fraction)
Sep 24 10:29 UTC (GMT)
753/752 already reduced (simplified) to lowest terms
753 > 752 => improper fraction

Rewrite:
753 ÷ 752 = 1 and remainder = 1 =>
753/752 = (1 × 752 + 1)/752 = 1 + 1/752 =
= 1 1/752, mixed number (mixed fraction)
Sep 24 10:29 UTC (GMT)
210/104 = (210 ÷ 2)/(104 ÷ 2) = 105/52;
105 > 52 => improper fraction

Rewrite:
105 ÷ 52 = 2 and remainder = 1 =>
105/52 = (2 × 52 + 1)/52 = 2 + 1/52 =
= 2 1/52, mixed number (mixed fraction)
Sep 24 10:29 UTC (GMT)
310/540 = (310 ÷ 10)/(540 ÷ 10) = 31/54 Sep 24 10:29 UTC (GMT)
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Tutoring: simplifying ordinary math fractions (reducing to lower terms)

Steps to simplify an ordinary fraction, to reduce it to its lowest terms

  • Factor the fraction's both numerator and denominator into prime factors.
  • Calculate fraction's both numerator and denominator greatest common factor, GCF (or greatest common divisor, GCD).
  • Divide fraction's both numerator and denominator by the greatest common factor GCF (divisor GCD). Fraction thus obtained is called a reduced fraction (simplified) to its lowest terms.

Simplifying ordinary math fractions (reducing to lower terms): steps to follow and examples


Why reducing fractions to lower terms (simplifying)?

Operations with fractions often involve fractions being brought to the same denominator and sometimes both numerators and denominators are large numbers. Doing calculations with such large numbers could be difficult. By simplifying (reducing) a fraction, both the numerator and denominator of the fraction are reduced to smaller values, much easier to work with, reducing the effort of working with fractions.