How to reduce (simplify) the common fraction 29/12 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:


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


12 = 22 × 3

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; 22 × 3) = 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.

Positive 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 ÷ 12 = 2 and remainder = 5 =>


29 = 2 × 12 + 5 =>


29/12 =


(2 × 12 + 5) / 12 =


2 + 5/12 =


5/12

As a decimal number:

5/12 =


2 + 5/12 =


2 + 5 ÷ 12 =


2.416666666667 ≈


2.42

As a percentage:

2.416666666667 =


2.416666666667 × 100/100 =


241.666666666667/100 =


241.666666666667% ≈


241.67%

Convert fractions to percentages, online calculator


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

As a positive improper fraction (numerator > denominator):
29/12 = 29/12

As a mixed number
(a whole number and a proper fraction, of the same sign):
29/12 = 5/12

As a decimal number:
29/122.42

As a percentage:
29/12241.67%

How to reduce (simplify) the common fraction: 38/16?


Writing numbers: point '.' used as a decimal mark;

Symbols: / fraction bar; ÷ divide; × multiply; + plus; ≈ approximation; = equal;

Reduce (simplify) ordinary fractions, online calculator

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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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