How to completely reduce (simplify) the fraction 15/6,226 to the lowest terms (its simplest form, the smallest possible numerator and denominator)? Write the result as a proper fraction, as a decimal number and as a percentage

Reduce (simplify) the fraction: 15/6,226

Detailed calculations below:

Fractions, brief introduction

A fraction consists of two numbers and the fraction bar: 15/6,226


The number above the fraction bar is the numerator: 15


The number under the fraction bar is the denominator: 6,226


The fraction bar means that the two numbers divide themselves:
15/6,226 = 15 ÷ 6,226


Divide the numerator by the denominator to get the value of the fraction:
The value = 15 ÷ 6,226


Percentages, short introduction

'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 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.


15 = 3 × 5
15 is not a prime number but a composite one.


6,226 = 2 × 11 × 283
6,226 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 (15; 6,226) = 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.


15/6,226 is a proper fraction.

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


Rewrite the fraction:

As a decimal number:

15/6,226 =


15 ÷ 6,226 ≈


0.002409251526


0


As a percentage:

0.002409251526 =


0.002409251526 × 100/100 =


0.240925152586/100 =


0.240925152586% ≈


0.24%


In other words:

1) Calculate the value of the fraction.


2) Multiply this number by 100.


3) Add the percent sign, %.



The final answer
This continues below...

The final answer:
:: Written in three ways ::

As a proper fraction:
15/6,226 = 15/6,226

As a decimal number:
15/6,2260.0024092515260

As a percentage:
15/6,2260.24%

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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.

Tutoring: simplifying fractions - reducing them to the lowest terms

Steps to simplify a fraction, to reduce it to its lowest terms:

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


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


Why reducing (simplifying) fractions to lower terms?


What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples