How To Completely Reduce (Simplify) the Fraction 150/3 to the Lowest Terms, Its Simplest Equivalent Form, Irreducible, With the Smallest Possible Numerator and Denominator (Prime to Each Other)? Write the Result as an Improper Fraction, as an Integer and as a Percentage
Reduce (simplify) the fraction: 150/3
To completely reduce (simplify) a fraction to its lowest terms, divide the numerator and the denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd)
To calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd), we perform the prime factorization of the two numbers.
The prime factorization of the two numbers:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
150 = 2 × 3 × 52
150 is not a prime number but a composite one.
3 is a prime number and cannot be broken down into other prime factors.
* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.
Calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd):
Multiply all the common prime factors, taken by their smallest exponents (powers).
gcf, hcf, gcd (150; 3) = 3
Divide the numerator and the denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd).
(2 × 3 × 52)/3 =
((2 × 3 × 52) ÷ 3) / (3 ÷ 3) =
(2 × 52)/1 =
(If the denominator is 1, it can be omitted)
The fraction is now completely reduced (simplified) to its lowest terms.
A fraction that is completely reduced (simplified) to its lowest terms (to its basic representation, to its simplest form) has the smallest possible numerator and denominator.
A fully reduced fraction is called an irreducible fraction and its numerator and denominator are coprime numbers.
50 = 50/1 is an improper fraction.
An improper fraction: the numerator is greater than or equal to the denominator.
Rewrite the result.
As an improper fraction
(the denominator = 1):
50 = 50/1
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.
50 × 100/100 =
(50 × 100)/100 =
The final answer:
:: Written in three ways ::
As an improper fraction:
150/3 = 50/1
As an integer:
150/3 = 50
As a percentage:
150/3 = 5,000%
Other similar operations with fractions reducing (simplification):
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.