How to reduce (simplify) to lowest terms ordinary (common) math fraction 1,256/128? Result written as: an improper fraction, a mixed number, a decimal number and a percentage

What is the fraction 1,256/128 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: 1,256/128


The number above the bar is the numerator: 1,256


The number below the bar is the denominator: 128


The fraction bar means that the two numbers are dividing themselves:
1,256/128 = 1,256 ÷ 128


Divide the numerator by the denominator to get fraction's value:
Value = 1,256 ÷ 128


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.


1,256 = 23 × 157;
1,256 is not a prime, is a composite number;


128 = 27;
128 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 (1,256; 128) = 23 = 8



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

1,256/128 =


(23 × 157)/27 =


((23 × 157) ÷ 23) / (27 ÷ 23) =


157/24 =


157/16


The fraction is now reduced to the lowest terms.

157/16 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.


157 ÷ 16 = 9 and remainder = 13 =>


157 = 9 × 16 + 13 =>


157/16 =


(9 × 16 + 13) / 16 =


(9 × 16) / 16 + 13 / 16 =


9 + 13/16 =


13/16


As a decimal number:

13/16 =


9 + 13/16 =


9 + 13 ÷ 16 =


9.8125


9.81


As a percentage:

9.8125 =


9.8125 × 100/100 =


981.25/100 =


981.25%


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):
1,256/128 = 157/16

As a mixed number (mixed fraction)
(a whole number and a proper fraction, of the same sign):
1,256/128 = 13/16

As a decimal number:
1,256/128 = 9.81259.81

As a percentage:
1,256/128 = 981.25%

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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