How To Completely Reduce (Simplify) the Fraction 7,813/36 to the Lowest Terms, Its Simplest Equivalent Form, Irreducible, With the Smallest Possible Numerator and Denominator, That Are Prime to Each Other? Write the Result as an Improper Fraction, as a Mixed Number, as a Decimal Number and as a Percentage

Reduce (simplify) the fraction: 7,813/36

Detailed calculations below:

Fractions, brief introduction

A fraction consists of two numbers and the fraction bar: 7,813/36


The number above the fraction bar is the numerator: 7,813


The number under the fraction bar is the denominator: 36


The fraction bar means that the two numbers divide themselves:
7,813/36 = 7,813 ÷ 36


Divide the numerator by the denominator to get the value of the fraction:
The value = 7,813 ÷ 36


Percentages, short introduction

'Percent, p%' means 'p 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 will not change.



To completely reduce (simplify) a fraction to its lowest terms, divide the numerator and the denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd)

To calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd), we perform the prime factorization of the two numbers.


The prime factorization of the two numbers:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


7,813 = 13 × 601
7,813 is not a prime number but a composite one.

36 = 22 × 32
36 is not a prime number but a composite one.


* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.

* A composite number is a natural number that has at least one other factor than 1 and itself.



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

Multiply all the common prime factors, taken by their smallest exponents (powers).


But the two numbers have no common prime factors:

gcf, hcf, gcd (7,813; 36) = 1
Coprime numbers (prime to each other, relatively prime)



The fraction cannot be reduced (simplified)

The numerator and denominator of the fraction are relatively prime numbers (coprime, prime to each other).


The only common factor (divisor) of the two numbers is 1.


7,813/36 is an improper fraction.

An improper fraction: the numerator is greater than or equal to the denominator.


Rewrite the fraction:

As a mixed number (mixed fraction):

A mixed number: an integer and a proper fraction that have the same sign.


The original improper fraction is obtained by adding the integer number and the proper fraction.


A proper fraction: the numerator is smaller than the denominator.


7,813 ÷ 36 = 217 and Remainder = 1 =>


7,813 = 217 × 36 + 1 =>


7,813/36 =


(217 × 36 + 1) / 36 =


(217 × 36) / 36 + 1 / 36 =


217 + 1/36 =


217 1/36


As a decimal number:

Divide the numerator of the fraction by its denominator.

217 1/36 =


217 + 1/36 =


217 + 1 ÷ 36 ≈


217.027777777778


217.03


As a percentage:

Multiply the fraction's value by the fraction 100/100

217.027777777778 =


217.027777777778 × 100/100 =


21,702.777777777778/100 =


21,702.777777777778% ≈


21,702.78%


The final answer:
:: Written in four ways ::

As an improper fraction:
7,813/36 = 7,813/36

As a mixed number (mixed fraction):
7,813/36 = 217 1/36

As a decimal number:
7,813/36217.027777777778217.03

As a percentage:
7,813/3621,702.78%

Other similar operations with fractions reducing (simplification):


Online Calculator: Completely reduce (simplify) fraction to the lowest terms

To fully reduce (simplify) fractions to the lowest terms:

Divide the numerator and denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd).

Result written as a proper or an improper fraction, as a mixed number, as a decimal or an integer and as a percentage.

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Tutoring: simplifying fractions - reducing them to the lowest terms

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Example: reduce the fraction 315/1,155 as much as possible, simplify it to the lowest terms.

Why reducing (simplifying) fractions to lower terms?

Read the entire article >> Completely reduce (simplify) fractions to the lowest terms: Steps and Examples

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