How to reduce (simplify) to lowest terms ordinary (common) math fraction 328/100? Result written as: an improper fraction, a mixed number, a decimal number and a percentage

What is the fraction 328/100 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: 328/100


The number above the bar is the numerator: 328


The number below the bar is the denominator: 100


The fraction bar means that the two numbers are dividing themselves:
328/100 = 328 ÷ 100


Divide the numerator by the denominator to get fraction's value:
Value = 328 ÷ 100


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.


328 = 23 × 41;
328 is not a prime, is a composite number;


100 = 22 × 52;
100 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 (328; 100) = 22 = 4



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

328/100 =


(23 × 41)/(22 × 52) =


((23 × 41) ÷ 22) / ((22 × 52) ÷ 22) =


(2 × 41)/52 =


82/25


The fraction is now reduced to the lowest terms.

82/25 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.


82 ÷ 25 = 3 and remainder = 7 =>


82 = 3 × 25 + 7 =>


82/25 =


(3 × 25 + 7) / 25 =


(3 × 25) / 25 + 7 / 25 =


3 + 7/25 =


7/25


As a decimal number:

7/25 =


3 + 7/25 =


3 + 7 ÷ 25 =


3.28


As a percentage:

3.28 =


3.28 × 100/100 =


328/100 =


328%


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):
328/100 = 82/25

As a mixed number (mixed fraction)
(a whole number and a proper fraction, of the same sign):
328/100 = 7/25

As a decimal number:
328/100 = 3.28

As a percentage:
328/100 = 328%

More operations of this kind:

Online calculator: reduce (simplify) fractions

Latest fractions reduced (simplified) to the lowest terms

328/100 = (328 ÷ 4)/(100 ÷ 4) = 82/25;
82 > 25 => improper fraction

Rewrite:
82 ÷ 25 = 3 and remainder = 7 =>
82/25 = (3 × 25 + 7)/25 = 3 + 7/25 =
= 3 7/25, mixed number (mixed fraction)
Dec 02 21:25 UTC (GMT)
4,843/3,435 already reduced (simplified) to lowest terms
4,843 > 3,435 => improper fraction

Rewrite:
4,843 ÷ 3,435 = 1 and remainder = 1,408 =>
4,843/3,435 = (1 × 3,435 + 1,408)/3,435 = 1 + 1,408/3,435 =
= 1 1,408/3,435, mixed number (mixed fraction)
Dec 02 21:25 UTC (GMT)
461/54 already reduced (simplified) to lowest terms
461 > 54 => improper fraction

Rewrite:
461 ÷ 54 = 8 and remainder = 29 =>
461/54 = (8 × 54 + 29)/54 = 8 + 29/54 =
= 8 29/54, mixed number (mixed fraction)
Dec 02 21:25 UTC (GMT)
150/6,201 = (150 ÷ 3)/(6,201 ÷ 3) = 50/2,067 Dec 02 21:25 UTC (GMT)
666,666,667/1,000,000,000 already reduced (simplified) to lowest terms Dec 02 21:25 UTC (GMT)
9/4 already reduced (simplified) to lowest terms
9 > 4 => improper fraction

Rewrite:
9 ÷ 4 = 2 and remainder = 1 =>
9/4 = (2 × 4 + 1)/4 = 2 + 1/4 =
= 2 1/4, mixed number (mixed fraction)
Dec 02 21:25 UTC (GMT)
114/55 already reduced (simplified) to lowest terms
114 > 55 => improper fraction

Rewrite:
114 ÷ 55 = 2 and remainder = 4 =>
114/55 = (2 × 55 + 4)/55 = 2 + 4/55 =
= 2 4/55, mixed number (mixed fraction)
Dec 02 21:25 UTC (GMT)
9/70,146 = (9 ÷ 9)/(70,146 ÷ 9) = 1/7,794 Dec 02 21:25 UTC (GMT)
3,113/50 already reduced (simplified) to lowest terms
3,113 > 50 => improper fraction

Rewrite:
3,113 ÷ 50 = 62 and remainder = 13 =>
3,113/50 = (62 × 50 + 13)/50 = 62 + 13/50 =
= 62 13/50, mixed number (mixed fraction)
Dec 02 21:25 UTC (GMT)
1,125/16 already reduced (simplified) to lowest terms
1,125 > 16 => improper fraction

Rewrite:
1,125 ÷ 16 = 70 and remainder = 5 =>
1,125/16 = (70 × 16 + 5)/16 = 70 + 5/16 =
= 70 5/16, mixed number (mixed fraction)
Dec 02 21:25 UTC (GMT)
21,756/32,412 = (21,756 ÷ 444)/(32,412 ÷ 444) = 49/73 Dec 02 21:25 UTC (GMT)
754/580 = (754 ÷ 58)/(580 ÷ 58) = 13/10;
13 > 10 => improper fraction

Rewrite:
13 ÷ 10 = 1 and remainder = 3 =>
13/10 = (1 × 10 + 3)/10 = 1 + 3/10 =
= 1 3/10, mixed number (mixed fraction)
Dec 02 21:25 UTC (GMT)
100/1,000,000 = (100 ÷ 100)/(1,000,000 ÷ 100) = 1/10,000 Dec 02 21:25 UTC (GMT)
reduced fractions, see more...

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