How to reduce (simplify) the common fraction 232/16 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:


232 = 23 × 29


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.


gcf (23 × 29; 24) = 23

Calculate the greatest common factor, GCF, online calculator


Divide both the numerator and the denominator by their greatest common factor, GCF:

232/16 =


(23 × 29)/24 =


((23 × 29) ÷ 23) / (24 ÷ 23) =


29/2

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 ÷ 2 = 14 and remainder = 1 =>


29 = 14 × 2 + 1 =>


29/2 =


(14 × 2 + 1) / 2 =


14 + 1/2 =


14 1/2

As a decimal number:

14 1/2 =


14 + 1/2 =


14 + 1 ÷ 2 =


14.5

As a percentage:

14.5 =


14.5 × 100/100 =


1,450/100 =


1,450%

Convert fractions to percentages, online calculator


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

As a positive improper fraction (numerator > denominator):
232/16 = 29/2

As a mixed number
(a whole number and a proper fraction, of the same sign):
232/16 = 14 1/2

As a decimal number:
232/16 = 14.5

As a percentage:
232/16 = 1,450%

How to reduce (simplify) the common fraction: 239/18?


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

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

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

232/16 = (232 ÷ 8)/(16 ÷ 8) = 29/2
Improper fraction, rewrite it as a mixed number:
29 ÷ 2 = 14 and remainder = 1 =>
29/2 = (14 × 2 + 1)/2 = 14 + 1/2 = 14 1/2
Jul 02 22:21 UTC (GMT)
105/12 = (105 ÷ 3)/(12 ÷ 3) = 35/4
Improper fraction, rewrite it as a mixed number:
35 ÷ 4 = 8 and remainder = 3 =>
35/4 = (8 × 4 + 3)/4 = 8 + 3/4 = 8 3/4
Jul 02 22:21 UTC (GMT)
20/35 = (20 ÷ 5)/(35 ÷ 5) = 4/7 Jul 02 22:21 UTC (GMT)
49/3 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
49 ÷ 3 = 16 and remainder = 1 =>
49/3 = (16 × 3 + 1)/3 = 16 + 1/3 = 16 1/3
Jul 02 22:20 UTC (GMT)
71/40 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
71 ÷ 40 = 1 and remainder = 31 =>
71/40 = (1 × 40 + 31)/40 = 1 + 31/40 = 1 31/40
Jul 02 22:20 UTC (GMT)
30/36 = (30 ÷ 6)/(36 ÷ 6) = 5/6 Jul 02 22:20 UTC (GMT)
970/979 already reduced (simplified) Jul 02 22:20 UTC (GMT)
90/4,458 = (90 ÷ 6)/(4,458 ÷ 6) = 15/743 Jul 02 22:20 UTC (GMT)
8/4,297 already reduced (simplified) Jul 02 22:20 UTC (GMT)
3,199/370 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
3,199 ÷ 370 = 8 and remainder = 239 =>
3,199/370 = (8 × 370 + 239)/370 = 8 + 239/370 = 8 239/370
Jul 02 22:20 UTC (GMT)
681/2,673 = (681 ÷ 3)/(2,673 ÷ 3) = 227/891 Jul 02 22:20 UTC (GMT)
4,060/20 = (4,060 ÷ 20)/(20 ÷ 20) = 203/1 = 203 Jul 02 22:20 UTC (GMT)
3,449/106 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
3,449 ÷ 106 = 32 and remainder = 57 =>
3,449/106 = (32 × 106 + 57)/106 = 32 + 57/106 = 32 57/106
Jul 02 22:20 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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