How To Completely Reduce (Simplify) the Fraction 1/7 to the Lowest Terms, Its Simplest Equivalent Form, Irreducible, With the Smallest Possible Numerator and Denominator (Prime to Each Other)? Write the Result as a Proper Fraction, as a Decimal, and as a Percentage

Reduce (simplify) the fraction: 1/7

The fraction 1/7 cannot be further reduced (simplified)

It is already completely reduced (simplified) to its lowest terms (it has the smallest possible numerator and denominator).

1/7 is a proper fraction.

A proper fraction - the numerator is smaller than the denominator.


Rewrite the fraction:

As a decimal number:

Divide the numerator of the fraction by its denominator.

1/7 =

1 ÷ 7 ≈

0.142857142857 ≈

0.14


As a percentage:

Multiply the fraction's value by the fraction 100/100

100/100 = 100 ÷ 100 = 100% = 1

Multiply a number by the fraction 100/100,
... and its value will not change, only the form.


0.142857142857 =

0.142857142857 × 100/100 =

14.285714285714/100 =

14.285714285714% ≈

14.29%


The final answer:
:: Written in three ways ::

As a proper fraction
(the numerator is smaller than the denominator):
1/7 = 1/7

As a decimal number:
1/7 ≈ 0.142857142857 ≈ 0.14

As a percentage:
1/7 = 14.285714285714% ≈ 14.29%

Other similar operations with fractions reducing (simplification):

» Reduce (simplify) the fraction -4/-4 to the lowest terms (to its simplest form, the smallest possible numerator and denominator)

» Reduce (simplify) the fraction 8/14 to the lowest terms (to its simplest form, the smallest possible numerator and denominator)


Online Calculator: Completely reduce (simplify) fraction to the lowest terms

To fully reduce (simplify) fractions to the lowest terms:

Divide the numerator and denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd).

Result written as a proper or an improper fraction, as a mixed number, as a decimal or an integer and as a percentage.

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Tutoring: simplifying fractions - reducing them to the lowest terms

Steps to simplify a fraction, to reduce it to its lowest terms:

  • A fraction fully simplified, a fraction reduced to its lowest terms is a fraction that can no longer be simplified, it has been reduced to its simplest equivalent fraction, the one having the smallest numerator and denominator possible - prime to each other.
  • 1) Run the prime factorization of both the numerator and the denominator of the fraction.
  • 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 their greatest common factor, GCF (GCD).
  • The fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
  • A fraction reduced to its lowest terms may no longer be reduced and it is called an irreducible fraction.

Example: reduce the fraction 315/1,155 as much as possible, simplify it to the lowest terms.

  • 1) Run the prime factorization of both the numerator and the denominator of the fraction.

  • The numerator of the fraction is 315, its breaking down into prime factors is:
    315 = 3 × 3 × 5 × 7 = 32 × 5 × 7
  • The denominator of the fraction is 1,155, its breaking down into prime factors is:
    1,155 = 3 × 5 × 7 × 11.

  • 2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.

  • The greatest common factor, gcf (315; 1,155), is calculated by multiplying all the common prime factors of the numerator and the denominator, taken by their lowest powers (their lowest exponents):
  • GCF (315; 1,155) = (32 × 5 × 7; 3 × 5 × 7 × 11) = 3 × 5 × 7 = 105

  • 3) Divide both the numerator and the denominator of the fraction by their greatest common factor, GCF (GCD).

  • The numerator and denominator of the fraction are divided by their greatest common factor, GCF:
  • 315/1,155 =
    (32 × 5 × 7)/(3 × 5 × 7 × 11) =
    ((32 × 5 × 7) ÷ (3 × 5 × 7)) / ((3 × 5 × 7 × 11) ÷ (3 × 5 × 7)) =
    3/11
  • The fraction thus obtained is called a fraction reduced to the lowest terms.

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 reducing (simplifying) a fraction, both its numerator and denominator are reduced to smaller values, much easier to work with, which will decrease the overall effort of working with that fraction.

Read the entire article ⇒ Completely reduce (simplify) fractions to the lowest terms: Steps and Examples