Calculator: ordinary math fractions reducing to lowest terms (simplifying) explained. Final result written as a proper fraction or as an improper one and a mixed number, as an integer or a decimal, as a percentage

Online calculator: reduce (simplify) fractions

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

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

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

Latest fractions reduced (simplified) to the lowest terms

89/200 already reduced (simplified) to lowest terms Nov 25 19:41 UTC (GMT)
5/468 already reduced (simplified) to lowest terms Nov 25 19:41 UTC (GMT)
189/60 = (189 ÷ 3)/(60 ÷ 3) = 63/20;
63 > 20 => improper fraction

Rewrite:
63 ÷ 20 = 3 and remainder = 3 =>
63/20 = (3 × 20 + 3)/20 = 3 + 3/20 =
= 3 3/20, mixed number (mixed fraction)
Nov 25 19:41 UTC (GMT)
144/57 = (144 ÷ 3)/(57 ÷ 3) = 48/19;
48 > 19 => improper fraction

Rewrite:
48 ÷ 19 = 2 and remainder = 10 =>
48/19 = (2 × 19 + 10)/19 = 2 + 10/19 =
= 2 10/19, mixed number (mixed fraction)
Nov 25 19:41 UTC (GMT)
88/90 = (88 ÷ 2)/(90 ÷ 2) = 44/45 Nov 25 19:41 UTC (GMT)
40/75 = (40 ÷ 5)/(75 ÷ 5) = 8/15 Nov 25 19:41 UTC (GMT)
96/39 = (96 ÷ 3)/(39 ÷ 3) = 32/13;
32 > 13 => improper fraction

Rewrite:
32 ÷ 13 = 2 and remainder = 6 =>
32/13 = (2 × 13 + 6)/13 = 2 + 6/13 =
= 2 6/13, mixed number (mixed fraction)
Nov 25 19:41 UTC (GMT)
17/1,672,619,703 already reduced (simplified) to lowest terms Nov 25 19:41 UTC (GMT)
412/3 already reduced (simplified) to lowest terms
412 > 3 => improper fraction

Rewrite:
412 ÷ 3 = 137 and remainder = 1 =>
412/3 = (137 × 3 + 1)/3 = 137 + 1/3 =
= 137 1/3, mixed number (mixed fraction)
Nov 25 19:41 UTC (GMT)
62/29 already reduced (simplified) to lowest terms
62 > 29 => improper fraction

Rewrite:
62 ÷ 29 = 2 and remainder = 4 =>
62/29 = (2 × 29 + 4)/29 = 2 + 4/29 =
= 2 4/29, mixed number (mixed fraction)
Nov 25 19:41 UTC (GMT)
4/12 = (4 ÷ 4)/(12 ÷ 4) = 1/3 Nov 25 19:41 UTC (GMT)
2,720/35 = (2,720 ÷ 5)/(35 ÷ 5) = 544/7;
544 > 7 => improper fraction

Rewrite:
544 ÷ 7 = 77 and remainder = 5 =>
544/7 = (77 × 7 + 5)/7 = 77 + 5/7 =
= 77 5/7, mixed number (mixed fraction)
Nov 25 19:41 UTC (GMT)
45/153 = (45 ÷ 9)/(153 ÷ 9) = 5/17 Nov 25 19:41 UTC (GMT)
reduced fractions, see more...

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 (common) 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.

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

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