How to reduce (simplify) the common fraction - 51/13 to its simplest equivalent form, irreducible? Result written as an improper fraction, as a mixed number, as a decimal number and as a percentage %

To reduce a fraction divide the numerator and the denominator by their greatest common factor, GCF

Factor both the numerator and the denominator, break them down to prime factors:

51 = 3 × 17


13 is a prime number, it cannot be factored into other prime factors

Calculate the prime factors of numbers, online calculator


Calculate the greatest common factor, GCF:

Multiply all the common prime factors, by the lowest exponents.


But, the numerator and the denominator have no common factors.


gcf (3 × 17; 13) = 1

Calculate the greatest common factor, GCF, online calculator


The numerator and the denominator of the fraction are coprime numbers (no common prime factors, GCF = 1), the fraction cannot be reduced (simplified): irreducible fraction.

- 51/13 = - 51/13

Negative improper fraction (|numerator| > |denominator|)
Rewrite the fraction:

As a mixed number (also called a mixed fraction):

Mixed number = a whole number and a proper fraction, of the same sign.


Proper fraction = numerator smaller than denominator.


- 51 ÷ 13 = - 3 and remainder = - 12 =>


- 51 = - 3 × 13 - 12 =>


- 51/13 =


( - 3 × 13 - 12) / 13 =


- 3 - 12/13 =


- 3 12/13

As a decimal number:

- 3 12/13 =


- 3 - 12/13 =


- 3 - 12 ÷ 13 =


- 3.923076923077 ≈


- 3.92

As a percentage:

- 3.923076923077 =


- 3.923076923077 × 100/100 =


- 392.307692307692/100 =


- 392.307692307692% ≈


- 392.31%

Convert fractions to percentages, online calculator


The final answer:
:: written in four ways ::

As a negative improper fraction (|numerator| > |denominator|):
- 51/13 = - 51/13

As a mixed number
(a whole number and a proper fraction, of the same sign):
- 51/13 = - 3 12/13

As a decimal number:
- 51/13 - 3.92

As a percentage:
- 51/13 - 392.31%

How to reduce (simplify) the common fraction: - 43/22?


Writing numbers: point '.' used as a decimal mark; two vertical bars surrounding a number, |n|, is the symbol for the absolute value of that number;

Symbols: / fraction bar; ÷ divide; × multiply; - minus; ≈ approximation; = equal;

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

- 51/13 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 51 ÷ 13 = - 3 and remainder = - 12 =>
- 51/13 = ( - 3 × 13 - 12)/13 = - 3 - 12/13 = - 3 12/13
Jul 02 19:56 UTC (GMT)
248/3,446 = (248 ÷ 2)/(3,446 ÷ 2) = 124/1,723 Jul 02 19:55 UTC (GMT)
135/10 = (135 ÷ 5)/(10 ÷ 5) = 27/2
Improper fraction, rewrite it as a mixed number:
27 ÷ 2 = 13 and remainder = 1 =>
27/2 = (13 × 2 + 1)/2 = 13 + 1/2 = 13 1/2
Jul 02 19:55 UTC (GMT)
595/18 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
595 ÷ 18 = 33 and remainder = 1 =>
595/18 = (33 × 18 + 1)/18 = 33 + 1/18 = 33 1/18
Jul 02 19:55 UTC (GMT)
121/4 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
121 ÷ 4 = 30 and remainder = 1 =>
121/4 = (30 × 4 + 1)/4 = 30 + 1/4 = 30 1/4
Jul 02 19:55 UTC (GMT)
28/463 already reduced (simplified) Jul 02 19:55 UTC (GMT)
4,916/156 = (4,916 ÷ 4)/(156 ÷ 4) = 1,229/39
Improper fraction, rewrite it as a mixed number:
1,229 ÷ 39 = 31 and remainder = 20 =>
1,229/39 = (31 × 39 + 20)/39 = 31 + 20/39 = 31 20/39
Jul 02 19:55 UTC (GMT)
- 21/10 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 21 ÷ 10 = - 2 and remainder = - 1 =>
- 21/10 = ( - 2 × 10 - 1)/10 = - 2 - 1/10 = - 2 1/10
Jul 02 19:55 UTC (GMT)
3,465/165 = (3,465 ÷ 165)/(165 ÷ 165) = 21/1 = 21 Jul 02 19:55 UTC (GMT)
41/20 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
41 ÷ 20 = 2 and remainder = 1 =>
41/20 = (2 × 20 + 1)/20 = 2 + 1/20 = 2 1/20
Jul 02 19:55 UTC (GMT)
180/1,421 already reduced (simplified) Jul 02 19:55 UTC (GMT)
14/41 already reduced (simplified) Jul 02 19:55 UTC (GMT)
6/15 = (6 ÷ 3)/(15 ÷ 3) = 2/5 Jul 02 19:55 UTC (GMT)
see more... reduced fractions

Fractions reducing to lower terms (simplifying). Equivalent fractions

Let's learn by an example, let's simplify the fraction: 12/16

  • Numerator of the fraction. The number that is above the fraction bar, 12, is called the numerator of the fraction;
  • Denominator of the fraction. The number that is below the fraction bar, 16, is called the denominator of the fraction;
  • The value of the fraction. Fraction 12/16 shows us in how many equal parts the number above the fraction bar, 12, is being divided: into 16 equal parts. Thus, the value of the fraction is calculated as:
  • 12 ÷ 16 = 0.75
  • We notice that the two numbers, the numerator and the denominator, are dividing themselves without any remainder by 2, so we divide them by the same number, 2:
  • 12/16 = (12 ÷ 2)/(16 ÷ 2) = 6/8
  • The value of the fraction 6/8 is calculated as:
  • 6 ÷ 8 = 0.75
  • We notice that the value of the fraction 6/8 is equal to that of the fraction 12/16, namely 0.75
  • Reduced (simplified) fraction, Equivalent fraction. The new fraction, 6/8, is equivalent to the original one, 12/16, that is, it represents the same value or proportion of the whole, and it was calculated out of the original fraction by reducing it (simplifying it): both the numerator and the denominator of the fraction were divided by the number 2.
  • Common factor (divisor). The number 2 that was used to divide the two numbers that make up the fraction is called a common factor or a divisor of the numerator and the denominator of the fraction.
  • Find all the divisors of a number or all the common factors of two numbers, online.
  • The reduced fraction has now a numerator that is equal to 6 and a denominator that is equal to 8.
  • We also notice that the two new numbers, the new numerator and the new denominator, 6 and 8, are also dividing themselves without any remainder by 2 (2 is a common factor of 6 and 8), so we divide them again by 2:
  • 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
  • The value of the fraction 3/4 is calculated as:
  • 3 ÷ 4 = 0.75
  • The new fraction, 3/4, is a reduced fraction (a simplified fraction) and an equivalent of the fractions 12/16 and 6/8
  • Irreducible fraction. Fraction 3/4 is also called an irreducible fraction, in another words it could no longer be reduced or simplified, it is in its simplest form, the numbers 3 and 4, the numerator and the denominator of the fraction, are coprime numbers (prime to each other), not having any common factors other than 1.
  • Reduce fractions to lower terms (simplify), online, with explanations.

... Read the rest of this article, here: How to reduce (simplify) common fractions?

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