How to reduce (simplify) fraction 105/100 to lowest terms? Write it as an improper fraction, a mixed number, a decimal number, a percentage

Reduce: 105/100

Detailed calculations below:

Introduction. Fractions

A fraction consists of two numbers and a fraction bar: 105/100


The number above the bar is the numerator: 105


The number below the bar is the denominator: 100


The fraction bar means that the two numbers are dividing themselves:
105/100 = 105 ÷ 100


Divide the numerator by the denominator to get fraction's value:
Value = 105 ÷ 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.


105 = 3 × 5 × 7;
105 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 (105; 100) = 5



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

105/100 =


(3 × 5 × 7)/(22 × 52) =


((3 × 5 × 7) ÷ 5) / ((22 × 52) ÷ 5) =


(3 × 7)/(22 × 5) =


21/20


The fraction is now reduced to the lowest terms.

21/20 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.


21 ÷ 20 = 1 and remainder = 1 =>


21 = 1 × 20 + 1 =>


21/20 =


(1 × 20 + 1) / 20 =


(1 × 20) / 20 + 1 / 20 =


1 + 1/20 =


1/20


As a decimal number:

1/20 =


1 + 1/20 =


1 + 1 ÷ 20 =


1.05


As a percentage:

1.05 =


1.05 × 100/100 =


105/100 =


105%


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):
105/100 = 21/20

As a mixed number (mixed fraction)
(a whole number and a proper fraction, of the same sign):
105/100 = 1/20

As a decimal number:
105/100 = 1.05

As a percentage:
105/100 = 105%

More operations of this kind:

Online calculator: reduce (simplify) fractions

Latest fractions reduced (simplified) to the lowest terms

How to reduce (simplify) fraction: 22/49? Feb 25 13:42 UTC (GMT)
How to reduce (simplify) fraction: 103,351/18? Feb 25 13:42 UTC (GMT)
How to reduce (simplify) fraction: 105/100? Feb 25 13:42 UTC (GMT)
How to reduce (simplify) fraction: 4,294/169? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 12/295? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 1,817/40? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 20/2? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 36/60? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 16,384/8,194? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 100/9? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 90/72? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 75/35? Feb 25 13:41 UTC (GMT)
How to reduce (simplify) fraction: 496/244? Feb 25 13:41 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