How to reduce (simplify) to lowest terms ordinary (common) math fraction 48/8? Result written as: an improper fraction, an integer and a percentage

What is the fraction 48/8 written as an equivalent reduced fraction, as an integer number and as a percent value?

Detailed calculations below:

Introduction. Fractions

A fraction consists of two numbers and a fraction bar: 48/8


The number above the bar is the numerator: 48


The number below the bar is the denominator: 8


The fraction bar means that the two numbers are dividing themselves:
48/8 = 48 ÷ 8


Divide the numerator by the denominator to get fraction's value:
Value = 48 ÷ 8


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.


48 = 24 × 3;
48 is not a prime, is a composite number;


8 = 23;
8 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 (48; 8) = 23 = 8



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

48/8 =


(24 × 3)/23 =


((24 × 3) ÷ 23) / (23 ÷ 23) =


(2 × 3)/1 =


6/1 =


6


When the denominator is 1 it can be omitted.


The fraction is now reduced to the lowest terms.

6 = 6/1 is an improper fraction.

An improper fraction: numerator larger than denominator.


Rewrite the end result, continued below...

Rewrite the end result:

As an improper fraction
(denominator = 1):

6 = 6/1


As a percentage:

6 =


6 × 100/100 =


(6 × 100)/100 =


600/100 =


600%


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 three ways ::

As an improper fraction
(numerator larger than denominator):
48/8 = 6/1

As an integer:
48/8 = 6

As a percentage:
48/8 = 600%

More operations of this kind:

Online calculator: reduce (simplify) fractions

Latest fractions reduced (simplified) to the lowest terms

48/8 = (48 ÷ 8)/(8 ÷ 8) = 6 Dec 02 21:42 UTC (GMT)
40/79,296 = (40 ÷ 8)/(79,296 ÷ 8) = 5/9,912 Dec 02 21:42 UTC (GMT)
59/56 already reduced (simplified) to lowest terms
59 > 56 => improper fraction

Rewrite:
59 ÷ 56 = 1 and remainder = 3 =>
59/56 = (1 × 56 + 3)/56 = 1 + 3/56 =
= 1 3/56, mixed number (mixed fraction)
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87/4 already reduced (simplified) to lowest terms
87 > 4 => improper fraction

Rewrite:
87 ÷ 4 = 21 and remainder = 3 =>
87/4 = (21 × 4 + 3)/4 = 21 + 3/4 =
= 21 3/4, mixed number (mixed fraction)
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52,264/100,000,000,000 = (52,264 ÷ 8)/(100,000,000,000 ÷ 8) = 6,533/12,500,000,000 Dec 02 21:42 UTC (GMT)
8/2 = (8 ÷ 2)/(2 ÷ 2) = 4 Dec 02 21:42 UTC (GMT)
35/100 = (35 ÷ 5)/(100 ÷ 5) = 7/20 Dec 02 21:42 UTC (GMT)
3,861/16 already reduced (simplified) to lowest terms
3,861 > 16 => improper fraction

Rewrite:
3,861 ÷ 16 = 241 and remainder = 5 =>
3,861/16 = (241 × 16 + 5)/16 = 241 + 5/16 =
= 241 5/16, mixed number (mixed fraction)
Dec 02 21:42 UTC (GMT)
57/21 = (57 ÷ 3)/(21 ÷ 3) = 19/7;
19 > 7 => improper fraction

Rewrite:
19 ÷ 7 = 2 and remainder = 5 =>
19/7 = (2 × 7 + 5)/7 = 2 + 5/7 =
= 2 5/7, mixed number (mixed fraction)
Dec 02 21:42 UTC (GMT)
484/63,967 already reduced (simplified) to lowest terms Dec 02 21:42 UTC (GMT)
944/410 = (944 ÷ 2)/(410 ÷ 2) = 472/205;
472 > 205 => improper fraction

Rewrite:
472 ÷ 205 = 2 and remainder = 62 =>
472/205 = (2 × 205 + 62)/205 = 2 + 62/205 =
= 2 62/205, mixed number (mixed fraction)
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14,641/10,000 already reduced (simplified) to lowest terms
14,641 > 10,000 => improper fraction

Rewrite:
14,641 ÷ 10,000 = 1 and remainder = 4,641 =>
14,641/10,000 = (1 × 10,000 + 4,641)/10,000 = 1 + 4,641/10,000 =
= 1 4,641/10,000, mixed number (mixed fraction)
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1,076/2,773 already reduced (simplified) to lowest terms Dec 02 21:42 UTC (GMT)
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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