How to reduce (simplify) the common fraction - 81/16 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:

in the notation with exponents:


81 = 34


16 = 24

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 (34; 24) = 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.

- 81/16 = - 81/16

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.


- 81 ÷ 16 = - 5 and remainder = - 1 =>


- 81 = - 5 × 16 - 1 =>


- 81/16 =


( - 5 × 16 - 1) / 16 =


- 5 - 1/16 =


- 5 1/16

As a decimal number:

- 5 1/16 =


- 5 - 1/16 =


- 5 - 1 ÷ 16 =


- 5.0625 ≈


- 5.06

As a percentage:

- 5.0625 =


- 5.0625 × 100/100 =


- 506.25/100 =


- 506.25%

Convert fractions to percentages, online calculator


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

As a negative improper fraction (|numerator| > |denominator|):
- 81/16 = - 81/16

As a mixed number
(a whole number and a proper fraction, of the same sign):
- 81/16 = - 5 1/16

As a decimal number:
- 81/16 - 5.06

As a percentage:
- 81/16 = - 506.25%

How to reduce (simplify) the common fraction: - 77/24?


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

- 81/16 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 81 ÷ 16 = - 5 and remainder = - 1 =>
- 81/16 = ( - 5 × 16 - 1)/16 = - 5 - 1/16 = - 5 1/16
Jul 02 17:51 UTC (GMT)
9/30 = (9 ÷ 3)/(30 ÷ 3) = 3/10 Jul 02 17:50 UTC (GMT)
335/365 = (335 ÷ 5)/(365 ÷ 5) = 67/73 Jul 02 17:50 UTC (GMT)
3,578/3,773 already reduced (simplified) Jul 02 17:50 UTC (GMT)
835/14 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
835 ÷ 14 = 59 and remainder = 9 =>
835/14 = (59 × 14 + 9)/14 = 59 + 9/14 = 59 9/14
Jul 02 17:50 UTC (GMT)
12/1,048 = (12 ÷ 4)/(1,048 ÷ 4) = 3/262 Jul 02 17:50 UTC (GMT)
180/20 = (180 ÷ 20)/(20 ÷ 20) = 9/1 = 9 Jul 02 17:50 UTC (GMT)
301/2 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
301 ÷ 2 = 150 and remainder = 1 =>
301/2 = (150 × 2 + 1)/2 = 150 + 1/2 = 150 1/2
Jul 02 17:50 UTC (GMT)
- 125/27 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 125 ÷ 27 = - 4 and remainder = - 17 =>
- 125/27 = ( - 4 × 27 - 17)/27 = - 4 - 17/27 = - 4 17/27
Jul 02 17:50 UTC (GMT)
- 13/4 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 13 ÷ 4 = - 3 and remainder = - 1 =>
- 13/4 = ( - 3 × 4 - 1)/4 = - 3 - 1/4 = - 3 1/4
Jul 02 17:50 UTC (GMT)
- 14/3 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 14 ÷ 3 = - 4 and remainder = - 2 =>
- 14/3 = ( - 4 × 3 - 2)/3 = - 4 - 2/3 = - 4 2/3
Jul 02 17:50 UTC (GMT)
- 18/5 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 18 ÷ 5 = - 3 and remainder = - 3 =>
- 18/5 = ( - 3 × 5 - 3)/5 = - 3 - 3/5 = - 3 3/5
Jul 02 17:50 UTC (GMT)
13/3,628 already reduced (simplified) Jul 02 17:50 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?

More on ordinary (common) math fractions theory: