How to reduce (simplify) the common fraction 30,000,332/30,000,041 to its simplest equivalent form, irreducible? Result written as an improper fraction, as a mixed number, as a decimal number and as a percentage %
Reduce (simplify) 30,000,332/30,000,041
Detailed calculations and explanations, below
Ordinary fractions. Introduction
The fraction consists of two numbers and a fraction bar: 30,000,332/30,000,041
The number above the bar is called numerator: 30,000,332
The number below the bar is called denominator: 30,000,041
The fraction bar means that the two numbers are dividing themselves.
To get fraction's value divide the numerator by the denominator: Value = 30,000,332 ÷ 30,000,041
To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF
To calculate the greatest common factor, GCF:
1. Build the prime factorizations of the numerator and denominator.
2. Multiply all the common prime factors, by the lowest exponents.
Factor both the numerator and denominator, break them down to prime factors:
Prime Factorization of a number: finding the prime numbers that multiply together to make that number.
In exponential notation: 30,000,332 = 2 × 2 × 53 × 141,511 = 22 × 53 × 141,511; 30,000,332 is a composite number;
30,000,041 is a prime number, it cannot be factored into other prime factors;
* Positive integers that are only dividing by themselves and 1 are called prime numbers. * A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.
Fractions reducing to lower terms (simplifying). Equivalent fractions
Let's learn by an example, let's simplify the fraction: 12/16
Numerator of the fraction. The number that is above the fraction bar, 12, is called the numerator of the fraction;
Denominator of the fraction. The number that is below the fraction bar, 16, is called the denominator of the fraction;
The value of the fraction. Fraction 12/16 shows us in how many equal parts the number above the fraction bar, 12, is being divided: into 16 equal parts. Thus, the value of the fraction is calculated as:
12 ÷ 16 = 0.75
We notice that the two numbers, the numerator and the denominator, are dividing themselves without any remainder by 2, so we divide them by the same number, 2:
12/16 = (12 ÷ 2)/(16 ÷ 2) = 6/8
The value of the fraction 6/8 is calculated as:
6 ÷ 8 = 0.75
We notice that the value of the fraction 6/8 is equal to that of the fraction 12/16, namely 0.75
Reduced (simplified) fraction, Equivalent fraction. The new fraction, 6/8, is equivalent to the original one, 12/16, that is, it represents the same value or proportion of the whole, and it was calculated out of the original fraction by reducing it (simplifying it): both the numerator and the denominator of the fraction were divided by the number 2.
Common factor (divisor). The number 2 that was used to divide the two numbers that make up the fraction is called a common factor or a divisor of the numerator and the denominator of the fraction.
The reduced fraction has now a numerator that is equal to 6 and a denominator that is equal to 8.
We also notice that the two new numbers, the new numerator and the new denominator, 6 and 8, are also dividing themselves without any remainder by 2 (2 is a common factor of 6 and 8), so we divide them again by 2:
6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
The value of the fraction 3/4 is calculated as:
3 ÷ 4 = 0.75
The new fraction, 3/4, is a reduced fraction (a simplified fraction) and an equivalent of the fractions 12/16 and 6/8
Irreducible fraction. Fraction 3/4 is also called an irreducible fraction, in another words it could no longer be reduced or simplified, it is in its simplest form, the numbers 3 and 4, the numerator and the denominator of the fraction, are coprime numbers (prime to each other), not having any common factors other than 1.