How to reduce (simplify) the common fraction - 81/2 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


2 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 (34; 2) = 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.

- 81/2 = - 81/2

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 ÷ 2 = - 40 and remainder = - 1 =>


- 81 = - 40 × 2 - 1 =>


- 81/2 =


( - 40 × 2 - 1) / 2 =


- 40 - 1/2 =


- 40 1/2

As a decimal number:

- 40 1/2 =


- 40 - 1/2 =


- 40 - 1 ÷ 2 =


- 40.5

As a percentage:

- 40.5 =


- 40.5 × 100/100 =


- 4,050/100 =


- 4,050%

Convert fractions to percentages, online calculator


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

As a negative improper fraction (|numerator| > |denominator|):
- 81/2 = - 81/2

As a mixed number
(a whole number and a proper fraction, of the same sign):
- 81/2 = - 40 1/2

As a decimal number:
- 81/2 = - 40.5

As a percentage:
- 81/2 = - 4,050%

How to reduce (simplify) the common fraction: - 78/12?


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; = equal;

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

- 81/2 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 81 ÷ 2 = - 40 and remainder = - 1 =>
- 81/2 = ( - 40 × 2 - 1)/2 = - 40 - 1/2 = - 40 1/2
Oct 29 23:40 UTC (GMT)
6/736 = (6 ÷ 2)/(736 ÷ 2) = 3/368 Oct 29 23:40 UTC (GMT)
4,156/100 = (4,156 ÷ 4)/(100 ÷ 4) = 1,039/25
Improper fraction, rewrite it as a mixed number:
1,039 ÷ 25 = 41 and remainder = 14 =>
1,039/25 = (41 × 25 + 14)/25 = 41 + 14/25 = 41 14/25
Oct 29 23:40 UTC (GMT)
43/24 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
43 ÷ 24 = 1 and remainder = 19 =>
43/24 = (1 × 24 + 19)/24 = 1 + 19/24 = 1 19/24
Oct 29 23:40 UTC (GMT)
- 64/512 = - (64 ÷ 64)/(512 ÷ 64) = - 1/8 Oct 29 23:40 UTC (GMT)
2,200/15 = (2,200 ÷ 5)/(15 ÷ 5) = 440/3
Improper fraction, rewrite it as a mixed number:
440 ÷ 3 = 146 and remainder = 2 =>
440/3 = (146 × 3 + 2)/3 = 146 + 2/3 = 146 2/3
Oct 29 23:40 UTC (GMT)
- 137/57 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 137 ÷ 57 = - 2 and remainder = - 23 =>
- 137/57 = ( - 2 × 57 - 23)/57 = - 2 - 23/57 = - 2 23/57
Oct 29 23:40 UTC (GMT)
119/256 already reduced (simplified) Oct 29 23:40 UTC (GMT)
3/17 already reduced (simplified) Oct 29 23:40 UTC (GMT)
2,163/42 = (2,163 ÷ 21)/(42 ÷ 21) = 103/2
Improper fraction, rewrite it as a mixed number:
103 ÷ 2 = 51 and remainder = 1 =>
103/2 = (51 × 2 + 1)/2 = 51 + 1/2 = 51 1/2
Oct 29 23:39 UTC (GMT)
- 398/45 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 398 ÷ 45 = - 8 and remainder = - 38 =>
- 398/45 = ( - 8 × 45 - 38)/45 = - 8 - 38/45 = - 8 38/45
Oct 29 23:39 UTC (GMT)
- 11/650 already reduced (simplified) Oct 29 23:39 UTC (GMT)
9/16 already reduced (simplified) Oct 29 23:39 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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