To reduce a fraction to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF
To calculate the greatest common factor, GCF:
- 1. Factor the numerator and the denominator (into prime factors), build their prime factorizations.
- 2. Multiply all their common prime factors, taken by the lowest exponents.
1. Factor the numerator and the denominator:
To factor a number (into prime factors) - or, in other words, to break it down to prime factors - or, in other words, to build its prime factorization: find the prime numbers that multiply together to get that number.
The prime factorizations:
Written with exponents:
94,028 = 2 × 2 × 11 × 2,137 = 22 × 11 × 2,137
94,028 is a composite number.
11 is a prime number, it cannot be factored (into other prime factors).
94,028/11 =
(94,028 ÷ 11) / (11 ÷ 11) =
8,548/1 =
8,548
* When it's 1, the denominator of the fraction can be omitted.
Yet another method to reduce the fraction
To reduce a fraction without calculating the GCF: factor its numerator and denominator, then all the common prime factors are easily identified and crossed out.
94,028/11 =
(22 × 11 × 2,137)/11 =
((22 × 11 × 2,137) ÷ 11) / (11 ÷ 11) =
(22 × 2,137)/1 =
(22 × 2,137) =
8,548
* When it's 1, the denominator of the fraction can be omitted.
As a percentage:
- A percentage value p% is equal to the fraction: p/100, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.
- To do that, multiply the number by the fraction 100/100.
- The value of the fraction 100/100 = 1, so by multiplying the number by this fraction the result is not changing, only the form.
8,548 =
8,548 × 100/100 =
(8,548 × 100)/100 =
854,800/100 =
854,800%
- In other words:
- (1) Calculate the fraction's value, (2) multiply that number by 100, and (3) add the percent sign % to it.
The final answer:
written in three ways