How to reduce (simplify) fraction 22,022/1,395 to lowest terms? Write it as an improper fraction, a mixed number, a decimal number, a percentage

Reduce: 22,022/1,395

Detailed calculations below:

Introduction. Fractions

A fraction consists of two numbers and a fraction bar: 22,022/1,395


The number above the bar is the numerator: 22,022


The number below the bar is the denominator: 1,395


The fraction bar means that the two numbers are dividing themselves:
22,022/1,395 = 22,022 ÷ 1,395


Divide the numerator by the denominator to get fraction's value:
Value = 22,022 ÷ 1,395


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.

To calculate the greatest common factor, we build the prime factorization of the two numbers.


Integer numbers prime factorization:

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


22,022 = 2 × 7 × 112 × 13;
22,022 is not a prime, is a composite number;


1,395 = 32 × 5 × 31;
1,395 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).


But the two numbers have no common prime factors.


gcf, hcf, gcd (22,022; 1,395) = 1
coprime numbers (relatively prime)



Fraction's numerator and denominator are coprime numbers (no common prime factors). Fraction cannot be reduced (simplified) - irreducible.

22,022/1,395 is an improper fraction.

An improper fraction: numerator larger than denominator.


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.


22,022 ÷ 1,395 = 15 and remainder = 1,097 =>


22,022 = 15 × 1,395 + 1,097 =>


22,022/1,395 =


(15 × 1,395 + 1097) / 1,395 =


(15 × 1,395) / 1,395 + 1097 / 1,395 =


15 + 1,097/1,395 =


15 1,097/1,395


As a decimal number:

15 1,097/1,395 =


15 + 1,097/1,395 =


15 + 1,097 ÷ 1,395 ≈


15.786379928315


15.79


As a percentage:

15.786379928315 =


15.786379928315 × 100/100 =


1,578.637992831541/100 =


1,578.637992831541% ≈


1,578.64%


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):
22,022/1,395 = 22,022/1,395

As a mixed number (mixed fraction)
(a whole number and a proper fraction, of the same sign):
22,022/1,395 = 15 1,097/1,395

As a decimal number:
22,022/1,39515.78637992831515.79

As a percentage:
22,022/1,3951,578.64%

More operations of this kind:


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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