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

61/82 already reduced (simplified) to lowest terms Jul 16 14:29 UTC (GMT)
243/216 = (243 ÷ 27)/(216 ÷ 27) = 9/8;
9 > 8 => improper fraction

Rewrite:
9 ÷ 8 = 1 and remainder = 1 =>
9/8 = (1 × 8 + 1)/8 = 1 + 1/8 =
= 1 1/8, mixed number (mixed fraction)
Jul 16 14:29 UTC (GMT)
1,130/72 = (1,130 ÷ 2)/(72 ÷ 2) = 565/36;
565 > 36 => improper fraction

Rewrite:
565 ÷ 36 = 15 and remainder = 25 =>
565/36 = (15 × 36 + 25)/36 = 15 + 25/36 =
= 15 25/36, mixed number (mixed fraction)
Jul 16 14:29 UTC (GMT)
5/37,500,000 = (5 ÷ 5)/(37,500,000 ÷ 5) = 1/7,500,000 Jul 16 14:29 UTC (GMT)
61/80 already reduced (simplified) to lowest terms Jul 16 14:29 UTC (GMT)
16,800/7 = (16,800 ÷ 7)/(7 ÷ 7) = 2,400 Jul 16 14:29 UTC (GMT)
60/55 = (60 ÷ 5)/(55 ÷ 5) = 12/11;
12 > 11 => improper fraction

Rewrite:
12 ÷ 11 = 1 and remainder = 1 =>
12/11 = (1 × 11 + 1)/11 = 1 + 1/11 =
= 1 1/11, mixed number (mixed fraction)
Jul 16 14:29 UTC (GMT)
11,111/111,111 already reduced (simplified) to lowest terms Jul 16 14:29 UTC (GMT)
130/140 = (130 ÷ 10)/(140 ÷ 10) = 13/14 Jul 16 14:29 UTC (GMT)
5/25 = (5 ÷ 5)/(25 ÷ 5) = 1/5 Jul 16 14:29 UTC (GMT)
176/165 = (176 ÷ 11)/(165 ÷ 11) = 16/15;
16 > 15 => improper fraction

Rewrite:
16 ÷ 15 = 1 and remainder = 1 =>
16/15 = (1 × 15 + 1)/15 = 1 + 1/15 =
= 1 1/15, mixed number (mixed fraction)
Jul 16 14:29 UTC (GMT)
16,666/66,664 = (16,666 ÷ 16,666)/(66,664 ÷ 16,666) = 1/4 Jul 16 14:29 UTC (GMT)
5/200 = (5 ÷ 5)/(200 ÷ 5) = 1/40 Jul 16 14:29 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.