How to reduce (simplify) to lowest terms ordinary (common) math fraction 68/3,400? Result written as: a proper fraction, a decimal number and a percentage

What is the fraction 68/3,400 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: 68/3,400


The number above the bar is the numerator: 68


The number below the bar is the denominator: 3,400


The fraction bar means that the two numbers are dividing themselves:
68/3,400 = 68 ÷ 3,400


Divide the numerator by the denominator to get fraction's value:
Value = 68 ÷ 3,400


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.


68 = 22 × 17;
68 is not a prime, is a composite number;


3,400 = 23 × 52 × 17;
3,400 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 (68; 3,400) = 22 × 17 = 68



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

68/3,400 =


(22 × 17)/(23 × 52 × 17) =


((22 × 17) ÷ (22 × 17)) / ((23 × 52 × 17) ÷ (22 × 17)) =


1/(2 × 52) =


1/50


The fraction is now reduced to the lowest terms.

1/50 is a proper fraction.

A proper fraction: numerator smaller than denominator.


Rewrite the end result, continued below...

Rewrite the end result:

As a decimal number:

1/50 =


1 ÷ 50 =


0.02


As a percentage:

0.02 =


0.02 × 100/100 =


2/100 =


2%


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 a proper fraction
(numerator smaller than denominator):
68/3,400 = 1/50

As a decimal number:
68/3,400 = 0.02

As a percentage:
68/3,400 = 2%

More operations of this kind:

Online calculator: reduce (simplify) fractions

Latest fractions reduced (simplified) to the lowest terms

68/3,400 = (68 ÷ 68)/(3,400 ÷ 68) = 1/50 Nov 25 20:09 UTC (GMT)
73/92 already reduced (simplified) to lowest terms Nov 25 20:09 UTC (GMT)
1,955/3,910 = (1,955 ÷ 1,955)/(3,910 ÷ 1,955) = 1/2 Nov 25 20:09 UTC (GMT)
287/242 already reduced (simplified) to lowest terms
287 > 242 => improper fraction

Rewrite:
287 ÷ 242 = 1 and remainder = 45 =>
287/242 = (1 × 242 + 45)/242 = 1 + 45/242 =
= 1 45/242, mixed number (mixed fraction)
Nov 25 20:09 UTC (GMT)
5,111/2,610 already reduced (simplified) to lowest terms
5,111 > 2,610 => improper fraction

Rewrite:
5,111 ÷ 2,610 = 1 and remainder = 2,501 =>
5,111/2,610 = (1 × 2,610 + 2,501)/2,610 = 1 + 2,501/2,610 =
= 1 2,501/2,610, mixed number (mixed fraction)
Nov 25 20:09 UTC (GMT)
9/129 = (9 ÷ 3)/(129 ÷ 3) = 3/43 Nov 25 20:09 UTC (GMT)
288/375 = (288 ÷ 3)/(375 ÷ 3) = 96/125 Nov 25 20:09 UTC (GMT)
5,878/90 = (5,878 ÷ 2)/(90 ÷ 2) = 2,939/45;
2,939 > 45 => improper fraction

Rewrite:
2,939 ÷ 45 = 65 and remainder = 14 =>
2,939/45 = (65 × 45 + 14)/45 = 65 + 14/45 =
= 65 14/45, mixed number (mixed fraction)
Nov 25 20:09 UTC (GMT)
342/72 = (342 ÷ 18)/(72 ÷ 18) = 19/4;
19 > 4 => improper fraction

Rewrite:
19 ÷ 4 = 4 and remainder = 3 =>
19/4 = (4 × 4 + 3)/4 = 4 + 3/4 =
= 4 3/4, mixed number (mixed fraction)
Nov 25 20:09 UTC (GMT)
9/5 already reduced (simplified) to lowest terms
9 > 5 => improper fraction

Rewrite:
9 ÷ 5 = 1 and remainder = 4 =>
9/5 = (1 × 5 + 4)/5 = 1 + 4/5 =
= 1 4/5, mixed number (mixed fraction)
Nov 25 20:09 UTC (GMT)
150/750 = (150 ÷ 150)/(750 ÷ 150) = 1/5 Nov 25 20:09 UTC (GMT)
5/25 = (5 ÷ 5)/(25 ÷ 5) = 1/5 Nov 25 20:08 UTC (GMT)
1,216/192 = (1,216 ÷ 64)/(192 ÷ 64) = 19/3;
19 > 3 => improper fraction

Rewrite:
19 ÷ 3 = 6 and remainder = 1 =>
19/3 = (6 × 3 + 1)/3 = 6 + 1/3 =
= 6 1/3, mixed number (mixed fraction)
Nov 25 20:08 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