Calculator: ordinary math fractions reducing to lowest terms (simplifying) explained. Result as a proper, improper fraction (mixed number), decimal

Online calculator: reduce (simplify) fractions

How to reduce (simplify) to 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

Latest reduced (simplified) fractions

72/132 = (72 ÷ 12)/(132 ÷ 12) = 6/11 Jul 22 16:34 UTC (GMT)
55/22 = (55 ÷ 11)/(22 ÷ 11) = 5/2;
5 > 2 => improper fraction

Rewrite:
5 ÷ 2 = 2 and remainder = 1 =>
5/2 = (2 × 2 + 1)/2 = 2 + 1/2 =
= 2 1/2, mixed number (mixed fraction)
Jul 22 16:34 UTC (GMT)
3,476/5,172 = (3,476 ÷ 4)/(5,172 ÷ 4) = 869/1,293 Jul 22 16:34 UTC (GMT)
4,612/9 already reduced (simplified) to lowest terms
4,612 > 9 => improper fraction

Rewrite:
4,612 ÷ 9 = 512 and remainder = 4 =>
4,612/9 = (512 × 9 + 4)/9 = 512 + 4/9 =
= 512 4/9, mixed number (mixed fraction)
Jul 22 16:34 UTC (GMT)
60/96 = (60 ÷ 12)/(96 ÷ 12) = 5/8 Jul 22 16:34 UTC (GMT)
2/32 = (2 ÷ 2)/(32 ÷ 2) = 1/16 Jul 22 16:34 UTC (GMT)
189/63 = (189 ÷ 63)/(63 ÷ 63) = 3 Jul 22 16:34 UTC (GMT)
54/4 = (54 ÷ 2)/(4 ÷ 2) = 27/2;
27 > 2 => improper fraction

Rewrite:
27 ÷ 2 = 13 and remainder = 1 =>
27/2 = (13 × 2 + 1)/2 = 13 + 1/2 =
= 13 1/2, mixed number (mixed fraction)
Jul 22 16:34 UTC (GMT)
895/999 already reduced (simplified) to lowest terms Jul 22 16:34 UTC (GMT)
246/46 = (246 ÷ 2)/(46 ÷ 2) = 123/23;
123 > 23 => improper fraction

Rewrite:
123 ÷ 23 = 5 and remainder = 8 =>
123/23 = (5 × 23 + 8)/23 = 5 + 8/23 =
= 5 8/23, mixed number (mixed fraction)
Jul 22 16:34 UTC (GMT)
6,569/900 already reduced (simplified) to lowest terms
6,569 > 900 => improper fraction

Rewrite:
6,569 ÷ 900 = 7 and remainder = 269 =>
6,569/900 = (7 × 900 + 269)/900 = 7 + 269/900 =
= 7 269/900, mixed number (mixed fraction)
Jul 22 16:34 UTC (GMT)
74/48 = (74 ÷ 2)/(48 ÷ 2) = 37/24;
37 > 24 => improper fraction

Rewrite:
37 ÷ 24 = 1 and remainder = 13 =>
37/24 = (1 × 24 + 13)/24 = 1 + 13/24 =
= 1 13/24, mixed number (mixed fraction)
Jul 22 16:34 UTC (GMT)
6,714/493 already reduced (simplified) to lowest terms
6,714 > 493 => improper fraction

Rewrite:
6,714 ÷ 493 = 13 and remainder = 305 =>
6,714/493 = (13 × 493 + 305)/493 = 13 + 305/493 =
= 13 305/493, mixed number (mixed fraction)
Jul 22 16:34 UTC (GMT)
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Tutoring: simplifying ordinary math fractions (reducing to the lowest terms)

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

  • 1) Factor both the numerator and the denominator of the fraction into prime factors.
  • 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 the greatest common factor, GCF (GCD).
  • In conclusion: the fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
  • A fraction reduced to its lowest terms cannot be further reduced and it is called an irreducible fraction.

Read the full article >> Simplifying ordinary math fractions (reducing to lower terms): steps to follow and examples


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 simplifying (reducing) a fraction, both the numerator and denominator of a fraction are reduced to smaller values. Well, these values are much easier to work with, reducing the overall effort of working with fractions.