How to reduce (simplify) the common fraction - 29/21 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:

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


21 = 3 × 7

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 (29; 3 × 7) = 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.

- 29/21 = - 29/21

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.


- 29 ÷ 21 = - 1 and remainder = - 8 =>


- 29 = - 1 × 21 - 8 =>


- 29/21 =


( - 1 × 21 - 8) / 21 =


- 1 - 8/21 =


- 1 8/21

As a decimal number:

- 1 8/21 =


- 1 - 8/21 =


- 1 - 8 ÷ 21 =


- 1.380952380952 ≈


- 1.38

As a percentage:

- 1.380952380952 =


- 1.380952380952 × 100/100 =


- 138.095238095238/100 =


- 138.095238095238% ≈


- 138.1%

Convert fractions to percentages, online calculator


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

As a negative improper fraction (|numerator| > |denominator|):
- 29/21 = - 29/21

As a mixed number
(a whole number and a proper fraction, of the same sign):
- 29/21 = - 1 8/21

As a decimal number:
- 29/21 - 1.38

As a percentage:
- 29/21 - 138.1%

How to reduce (simplify) the common fraction: - 20/23?


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

- 29/21 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
- 29 ÷ 21 = - 1 and remainder = - 8 =>
- 29/21 = ( - 1 × 21 - 8)/21 = - 1 - 8/21 = - 1 8/21
Jun 03 21:34 UTC (GMT)
- 5/7 already reduced (simplified) Jun 03 21:34 UTC (GMT)
300/13 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
300 ÷ 13 = 23 and remainder = 1 =>
300/13 = (23 × 13 + 1)/13 = 23 + 1/13 = 23 1/13
Jun 03 21:34 UTC (GMT)
858/97 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
858 ÷ 97 = 8 and remainder = 82 =>
858/97 = (8 × 97 + 82)/97 = 8 + 82/97 = 8 82/97
Jun 03 21:34 UTC (GMT)
90/1,392 = (90 ÷ 6)/(1,392 ÷ 6) = 15/232 Jun 03 21:34 UTC (GMT)
125/75 = (125 ÷ 25)/(75 ÷ 25) = 5/3
Improper fraction, rewrite it as a mixed number:
5 ÷ 3 = 1 and remainder = 2 =>
5/3 = (1 × 3 + 2)/3 = 1 + 2/3 = 1 2/3
Jun 03 21:34 UTC (GMT)
1,378/1,342 = (1,378 ÷ 2)/(1,342 ÷ 2) = 689/671
Improper fraction, rewrite it as a mixed number:
689 ÷ 671 = 1 and remainder = 18 =>
689/671 = (1 × 671 + 18)/671 = 1 + 18/671 = 1 18/671
Jun 03 21:34 UTC (GMT)
87/2 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
87 ÷ 2 = 43 and remainder = 1 =>
87/2 = (43 × 2 + 1)/2 = 43 + 1/2 = 43 1/2
Jun 03 21:33 UTC (GMT)
1,236/24,310 = (1,236 ÷ 2)/(24,310 ÷ 2) = 618/12,155 Jun 03 21:33 UTC (GMT)
2,671/63 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
2,671 ÷ 63 = 42 and remainder = 25 =>
2,671/63 = (42 × 63 + 25)/63 = 42 + 25/63 = 42 25/63
Jun 03 21:33 UTC (GMT)
30/7 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
30 ÷ 7 = 4 and remainder = 2 =>
30/7 = (4 × 7 + 2)/7 = 4 + 2/7 = 4 2/7
Jun 03 21:33 UTC (GMT)
140/4,770 = (140 ÷ 10)/(4,770 ÷ 10) = 14/477 Jun 03 21:33 UTC (GMT)
31/18 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
31 ÷ 18 = 1 and remainder = 13 =>
31/18 = (1 × 18 + 13)/18 = 1 + 13/18 = 1 13/18
Jun 03 21:32 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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