How to reduce (simplify) the common fraction 71/32 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:


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


32 = 25

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 (71; 25) = 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.


71 ÷ 32 = 2 and remainder = 7 =>


71 = 2 × 32 + 7 =>


71/32 =


(2 × 32 + 7) / 32 =


2 + 7/32 =


7/32

As a decimal number:

7/32 =


2 + 7/32 =


2 + 7 ÷ 32 =


2.21875 ≈


2.22

As a percentage:

2.21875 =


2.21875 × 100/100 =


221.875/100 =


221.875% ≈


221.88%

Convert fractions to percentages, online calculator


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

As a positive improper fraction (numerator > denominator):
71/32 = 71/32

As a mixed number
(a whole number and a proper fraction, of the same sign):
71/32 = 7/32

As a decimal number:
71/322.22

As a percentage:
71/32221.88%

How to reduce (simplify) the common fraction: 78/39?


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

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

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

71/32 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
71 ÷ 32 = 2 and remainder = 7 =>
71/32 = (2 × 32 + 7)/32 = 2 + 7/32 = 2 7/32
Jul 02 19:22 UTC (GMT)
18/ - 6 = - (18 ÷ 6)/(6 ÷ 6) = - 3/1 = - 3 Jul 02 19:22 UTC (GMT)
49/30 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
49 ÷ 30 = 1 and remainder = 19 =>
49/30 = (1 × 30 + 19)/30 = 1 + 19/30 = 1 19/30
Jul 02 19:22 UTC (GMT)
50/30 = (50 ÷ 10)/(30 ÷ 10) = 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
Jul 02 19:22 UTC (GMT)
2,393/4 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
2,393 ÷ 4 = 598 and remainder = 1 =>
2,393/4 = (598 × 4 + 1)/4 = 598 + 1/4 = 598 1/4
Jul 02 19:21 UTC (GMT)
9/2,983 already reduced (simplified) Jul 02 19:21 UTC (GMT)
4,765/1,308 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
4,765 ÷ 1,308 = 3 and remainder = 841 =>
4,765/1,308 = (3 × 1,308 + 841)/1,308 = 3 + 841/1,308 = 3 841/1,308
Jul 02 19:21 UTC (GMT)
49/60 already reduced (simplified) Jul 02 19:21 UTC (GMT)
3/16 already reduced (simplified) Jul 02 19:21 UTC (GMT)
953/317 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
953 ÷ 317 = 3 and remainder = 2 =>
953/317 = (3 × 317 + 2)/317 = 3 + 2/317 = 3 2/317
Jul 02 19:21 UTC (GMT)
39/160 already reduced (simplified) Jul 02 19:21 UTC (GMT)
3,361/59 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
3,361 ÷ 59 = 56 and remainder = 57 =>
3,361/59 = (56 × 59 + 57)/59 = 56 + 57/59 = 56 57/59
Jul 02 19:21 UTC (GMT)
1,453/54 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
1,453 ÷ 54 = 26 and remainder = 49 =>
1,453/54 = (26 × 54 + 49)/54 = 26 + 49/54 = 26 49/54
Jul 02 19:20 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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