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

145/100 = (145 ÷ 5)/(100 ÷ 5) = 29/20;
29 > 20 => improper fraction

Rewrite:
29 ÷ 20 = 1 and remainder = 9 =>
29/20 = (1 × 20 + 9)/20 = 1 + 9/20 =
= 1 9/20, mixed number (mixed fraction)
May 24 07:47 UTC (GMT)
121/225 already reduced (simplified) to lowest terms May 24 07:47 UTC (GMT)
77/18 already reduced (simplified) to lowest terms
77 > 18 => improper fraction

Rewrite:
77 ÷ 18 = 4 and remainder = 5 =>
77/18 = (4 × 18 + 5)/18 = 4 + 5/18 =
= 4 5/18, mixed number (mixed fraction)
May 24 07:47 UTC (GMT)
458/20 = (458 ÷ 2)/(20 ÷ 2) = 229/10;
229 > 10 => improper fraction

Rewrite:
229 ÷ 10 = 22 and remainder = 9 =>
229/10 = (22 × 10 + 9)/10 = 22 + 9/10 =
= 22 9/10, mixed number (mixed fraction)
May 24 07:47 UTC (GMT)
5/45 = (5 ÷ 5)/(45 ÷ 5) = 1/9 May 24 07:46 UTC (GMT)
39/50 already reduced (simplified) to lowest terms May 24 07:46 UTC (GMT)
60/144 = (60 ÷ 12)/(144 ÷ 12) = 5/12 May 24 07:46 UTC (GMT)
132/54 = (132 ÷ 6)/(54 ÷ 6) = 22/9;
22 > 9 => improper fraction

Rewrite:
22 ÷ 9 = 2 and remainder = 4 =>
22/9 = (2 × 9 + 4)/9 = 2 + 4/9 =
= 2 4/9, mixed number (mixed fraction)
May 24 07:46 UTC (GMT)
10,200/10,600 = (10,200 ÷ 200)/(10,600 ÷ 200) = 51/53 May 24 07:46 UTC (GMT)
365/146 = (365 ÷ 73)/(146 ÷ 73) = 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)
May 24 07:46 UTC (GMT)
11/162 already reduced (simplified) to lowest terms May 24 07:46 UTC (GMT)
145/24 already reduced (simplified) to lowest terms
145 > 24 => improper fraction

Rewrite:
145 ÷ 24 = 6 and remainder = 1 =>
145/24 = (6 × 24 + 1)/24 = 6 + 1/24 =
= 6 1/24, mixed number (mixed fraction)
May 24 07:46 UTC (GMT)
6/9 = (6 ÷ 3)/(9 ÷ 3) = 2/3 May 24 07:46 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.