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

319/500 already reduced (simplified) to lowest terms Nov 21 08:23 UTC (GMT)
256/172 = (256 ÷ 4)/(172 ÷ 4) = 64/43;
64 > 43 => improper fraction

Rewrite:
64 ÷ 43 = 1 and remainder = 21 =>
64/43 = (1 × 43 + 21)/43 = 1 + 21/43 =
= 1 21/43, mixed number (mixed fraction)
Nov 21 08:23 UTC (GMT)
20/15 = (20 ÷ 5)/(15 ÷ 5) = 4/3;
4 > 3 => improper fraction

Rewrite:
4 ÷ 3 = 1 and remainder = 1 =>
4/3 = (1 × 3 + 1)/3 = 1 + 1/3 =
= 1 1/3, mixed number (mixed fraction)
Nov 21 08:23 UTC (GMT)
845/1,014 = (845 ÷ 169)/(1,014 ÷ 169) = 5/6 Nov 21 08:23 UTC (GMT)
25/40 = (25 ÷ 5)/(40 ÷ 5) = 5/8 Nov 21 08:23 UTC (GMT)
80/120 = (80 ÷ 40)/(120 ÷ 40) = 2/3 Nov 21 08:23 UTC (GMT)
15,215,200/8,008 = (15,215,200 ÷ 8,008)/(8,008 ÷ 8,008) = 1,900 Nov 21 08:23 UTC (GMT)
1,050/180 = (1,050 ÷ 30)/(180 ÷ 30) = 35/6;
35 > 6 => improper fraction

Rewrite:
35 ÷ 6 = 5 and remainder = 5 =>
35/6 = (5 × 6 + 5)/6 = 5 + 5/6 =
= 5 5/6, mixed number (mixed fraction)
Nov 21 08:23 UTC (GMT)
60/559 already reduced (simplified) to lowest terms Nov 21 08:23 UTC (GMT)
168/252 = (168 ÷ 84)/(252 ÷ 84) = 2/3 Nov 21 08:23 UTC (GMT)
1,840/1,240 = (1,840 ÷ 40)/(1,240 ÷ 40) = 46/31;
46 > 31 => improper fraction

Rewrite:
46 ÷ 31 = 1 and remainder = 15 =>
46/31 = (1 × 31 + 15)/31 = 1 + 15/31 =
= 1 15/31, mixed number (mixed fraction)
Nov 21 08:23 UTC (GMT)
936/864 = (936 ÷ 72)/(864 ÷ 72) = 13/12;
13 > 12 => improper fraction

Rewrite:
13 ÷ 12 = 1 and remainder = 1 =>
13/12 = (1 × 12 + 1)/12 = 1 + 1/12 =
= 1 1/12, mixed number (mixed fraction)
Nov 21 08:23 UTC (GMT)
109/901 already reduced (simplified) to lowest terms Nov 21 08:23 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.