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 reduced (simplified) fractions

10/4 = (10 ÷ 2)/(4 ÷ 2) = 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)
Apr 02 03:53 UTC (GMT)
60/84 = (60 ÷ 12)/(84 ÷ 12) = 5/7 Apr 02 03:53 UTC (GMT)
99/55 = (99 ÷ 11)/(55 ÷ 11) = 9/5;
9 > 5 => improper fraction

Rewrite:
9 ÷ 5 = 1 and remainder = 4 =>
9/5 = (1 × 5 + 4)/5 = 1 + 4/5 =
= 1 4/5, mixed number (mixed fraction)
Apr 02 03:53 UTC (GMT)
42/63 = (42 ÷ 21)/(63 ÷ 21) = 2/3 Apr 02 03:52 UTC (GMT)
2/11 already reduced (simplified) to lowest terms Apr 02 03:52 UTC (GMT)
26/65 = (26 ÷ 13)/(65 ÷ 13) = 2/5 Apr 02 03:52 UTC (GMT)
210/350 = (210 ÷ 70)/(350 ÷ 70) = 3/5 Apr 02 03:52 UTC (GMT)
45/63 = (45 ÷ 9)/(63 ÷ 9) = 5/7 Apr 02 03:52 UTC (GMT)
3/396 = (3 ÷ 3)/(396 ÷ 3) = 1/132 Apr 02 03:52 UTC (GMT)
4,596/175 already reduced (simplified) to lowest terms
4,596 > 175 => improper fraction

Rewrite:
4,596 ÷ 175 = 26 and remainder = 46 =>
4,596/175 = (26 × 175 + 46)/175 = 26 + 46/175 =
= 26 46/175, mixed number (mixed fraction)
Apr 02 03:52 UTC (GMT)
19,583/10,000 already reduced (simplified) to lowest terms
19,583 > 10,000 => improper fraction

Rewrite:
19,583 ÷ 10,000 = 1 and remainder = 9,583 =>
19,583/10,000 = (1 × 10,000 + 9,583)/10,000 = 1 + 9,583/10,000 =
= 1 9,583/10,000, mixed number (mixed fraction)
Apr 02 03:52 UTC (GMT)
9/6 = (9 ÷ 3)/(6 ÷ 3) = 3/2;
3 > 2 => improper fraction

Rewrite:
3 ÷ 2 = 1 and remainder = 1 =>
3/2 = (1 × 2 + 1)/2 = 1 + 1/2 =
= 1 1/2, mixed number (mixed fraction)
Apr 02 03:52 UTC (GMT)
35/55 = (35 ÷ 5)/(55 ÷ 5) = 7/11 Apr 02 03:52 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