How to reduce (simplify) to lowest terms ordinary (common) math fraction 526/4? Result written as: an improper fraction, a mixed number, a decimal number and a percentage

What is the fraction 526/4 written as an equivalent reduced fraction, as a decimal number and as a percent value?

Detailed calculations below:

Introduction. Fractions

A fraction consists of two numbers and a fraction bar: 526/4


The number above the bar is the numerator: 526


The number below the bar is the denominator: 4


The fraction bar means that the two numbers are dividing themselves:
526/4 = 526 ÷ 4


Divide the numerator by the denominator to get fraction's value:
Value = 526 ÷ 4


Introduction. Percent

'Percent (%)' means 'out of one hundred':


p% = p 'out of one hundred',


p% = p/100 = p ÷ 100


Note:

The fraction 100/100 = 100 ÷ 100 = 100% = 1


Multiply a number by the fraction 100/100,
... and its value doesn't change.



To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

Integer numbers prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


526 = 2 × 263;
526 is not a prime, is a composite number;


4 = 22;
4 is not a prime, is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.


Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

Multiply all the common prime factors, by the lowest exponents (if any).


gcf, hcf, gcd (526; 4) = 2



Divide both the numerator and the denominator by their greatest common factor.

526/4 =


(2 × 263)/22 =


((2 × 263) ÷ 2) / (22 ÷ 2) =


263/2


The fraction is now reduced to the lowest terms.

263/2 is an improper fraction.

An improper fraction: numerator larger than denominator.


Rewrite the end result, continued below...

Rewrite the fraction:

As a mixed number (mixed fraction):

A mixed number (mixed fraction): a whole number and a proper fraction, of the same sign.


A proper fraction: numerator smaller than denominator.


263 ÷ 2 = 131 and remainder = 1 =>


263 = 131 × 2 + 1 =>


263/2 =


(131 × 2 + 1) / 2 =


(131 × 2) / 2 + 1 / 2 =


131 + 1/2 =


131 1/2


As a decimal number:

131 1/2 =


131 + 1/2 =


131 + 1 ÷ 2 =


131.5


As a percentage:

131.5 =


131.5 × 100/100 =


13,150/100 =


13,150%


In other words:

1) Calculate fraction's value.


2) Multiply that number by 100.


3) Add the percent sign % to it.



Final answer
continued below...

Final answer:
:: written in four ways ::

As an improper fraction
(numerator larger than denominator):
526/4 = 263/2

As a mixed number (mixed fraction)
(a whole number and a proper fraction, of the same sign):
526/4 = 131 1/2

As a decimal number:
526/4 = 131.5

As a percentage:
526/4 = 13,150%

More operations of this kind:

Online calculator: reduce (simplify) fractions

Latest fractions reduced (simplified) to the lowest terms

4,110/30 = (4,110 ÷ 30)/(30 ÷ 30) = 137 Nov 25 19:12 UTC (GMT)
526/4 = (526 ÷ 2)/(4 ÷ 2) = 263/2;
263 > 2 => improper fraction

Rewrite:
263 ÷ 2 = 131 and remainder = 1 =>
263/2 = (131 × 2 + 1)/2 = 131 + 1/2 =
= 131 1/2, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
4,248/100 = (4,248 ÷ 4)/(100 ÷ 4) = 1,062/25;
1,062 > 25 => improper fraction

Rewrite:
1,062 ÷ 25 = 42 and remainder = 12 =>
1,062/25 = (42 × 25 + 12)/25 = 42 + 12/25 =
= 42 12/25, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
4,110/30 = (4,110 ÷ 30)/(30 ÷ 30) = 137 Nov 25 19:12 UTC (GMT)
36/54 = (36 ÷ 18)/(54 ÷ 18) = 2/3 Nov 25 19:12 UTC (GMT)
500/101 already reduced (simplified) to lowest terms
500 > 101 => improper fraction

Rewrite:
500 ÷ 101 = 4 and remainder = 96 =>
500/101 = (4 × 101 + 96)/101 = 4 + 96/101 =
= 4 96/101, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
40,332/33,340 = (40,332 ÷ 4)/(33,340 ÷ 4) = 10,083/8,335;
10,083 > 8,335 => improper fraction

Rewrite:
10,083 ÷ 8,335 = 1 and remainder = 1,748 =>
10,083/8,335 = (1 × 8,335 + 1,748)/8,335 = 1 + 1,748/8,335 =
= 1 1,748/8,335, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
930/100 = (930 ÷ 10)/(100 ÷ 10) = 93/10;
93 > 10 => improper fraction

Rewrite:
93 ÷ 10 = 9 and remainder = 3 =>
93/10 = (9 × 10 + 3)/10 = 9 + 3/10 =
= 9 3/10, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
373/180 already reduced (simplified) to lowest terms
373 > 180 => improper fraction

Rewrite:
373 ÷ 180 = 2 and remainder = 13 =>
373/180 = (2 × 180 + 13)/180 = 2 + 13/180 =
= 2 13/180, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
2,078/36 = (2,078 ÷ 2)/(36 ÷ 2) = 1,039/18;
1,039 > 18 => improper fraction

Rewrite:
1,039 ÷ 18 = 57 and remainder = 13 =>
1,039/18 = (57 × 18 + 13)/18 = 57 + 13/18 =
= 57 13/18, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
999/308 already reduced (simplified) to lowest terms
999 > 308 => improper fraction

Rewrite:
999 ÷ 308 = 3 and remainder = 75 =>
999/308 = (3 × 308 + 75)/308 = 3 + 75/308 =
= 3 75/308, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
999/308 already reduced (simplified) to lowest terms
999 > 308 => improper fraction

Rewrite:
999 ÷ 308 = 3 and remainder = 75 =>
999/308 = (3 × 308 + 75)/308 = 3 + 75/308 =
= 3 75/308, mixed number (mixed fraction)
Nov 25 19:12 UTC (GMT)
590/990 = (590 ÷ 10)/(990 ÷ 10) = 59/99 Nov 25 19:12 UTC (GMT)
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Tutoring: simplifying ordinary math fractions (reducing to the lowest terms)

Steps to simplify an ordinary fraction, to reduce it to its lowest terms:

  • 1) Factor both the numerator and the denominator of the fraction into prime factors.
  • 2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.
  • 3) Divide both the numerator and the denominator of the fraction by the greatest common factor, GCF (GCD).
  • In conclusion: the fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
  • A fraction reduced to its lowest terms cannot be further reduced and it is called an irreducible fraction.

Read the full article >> Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples


Why reducing (simplifying) fractions to lower terms?

  • When running operations with fractions we are often required to bring them to the same denominator, for example when adding, subtracting or comparing.
  • Sometimes both the numerators and the denominators of those fractions are large numbers and doing calculations with such numbers could be difficult.
  • By simplifying (reducing) a fraction, both the numerator and denominator of a fraction are reduced to smaller values. Well, these values are much easier to work with, reducing the overall effort of working with fractions.

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples