How to completely reduce (simplify) the fraction 7/3 to the lowest terms (its simplest form, the smallest possible numerator and denominator)? Write the result as an improper fraction, as a mixed number, as a decimal number and as a percentage

Reduce (simplify) the fraction: 7/3

Detailed calculations below:

Fractions, brief introduction.

A fraction consists of two numbers and the fraction bar: 7/3


The number above the fraction bar is the numerator: 7


The number under the fraction bar is the denominator: 3


The fraction bar means that the two numbers divide themselves:
7/3 = 7 ÷ 3


Divide the numerator by the denominator to get the value of the fraction:
The value = 7 ÷ 3


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.


7 is a prime number and cannot be broken down into other prime factors.


3 is a prime number and cannot be broken down into other prime factors.


* 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; 3) = 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.


7/3 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 ÷ 3 = 2 and Remainder = 1 =>


7 = 2 × 3 + 1 =>


7/3 =


(2 × 3 + 1) / 3 =


(2 × 3) / 3 + 1 / 3 =


2 + 1/3 =


1/3


As a decimal number:

1/3 =


2 + 1/3 =


2 + 1 ÷ 3 ≈


2.333333333333


2.33


As a percentage:

2.333333333333 =


2.333333333333 × 100/100 =


233.333333333333/100 =


233.333333333333% ≈


233.33%


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 four ways ::

As an improper fraction:
7/3 = 7/3

As a mixed number (mixed fraction):
7/3 = 1/3

As a decimal number:
7/32.3333333333332.33

As a percentage:
7/3233.33%

Other operations of this kind:


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.

The latest fractions that have been fully reduced (simplified) to their lowest terms (to their simplest form, the smallest possible numerator and denominator)

Reduce (simplify) the fraction: 7/3 = ? May 24 21:20 UTC (GMT)
Reduce (simplify) the fraction: 3/339,393,936 = ? May 24 21:20 UTC (GMT)
Reduce (simplify) the fraction: 328,000,000,003/36 = ? May 24 21:20 UTC (GMT)
Reduce (simplify) the fraction: 26/18 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 340/5,100 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 450,715/6 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 73,501/29,402 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 120/105,305,760 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 222/2,530,000 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 999,999/1,000,000 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 57/24 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 3,901/458 = ? May 24 21:19 UTC (GMT)
Reduce (simplify) the fraction: 7/21,732,560,850 = ? May 24 21:19 UTC (GMT)
The list of all the fractions that were fully reduced (simplified) to their lowest terms (to their simplest form, the smallest possible numerator and denominator)

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