Detailed calculations and explanations, below
Ordinary fractions. Introduction
The fraction consists of two numbers and a fraction bar: 31/40
The number above the bar is called numerator: 31
The number below the bar is called denominator: 40
The fraction bar means that the two numbers are dividing themselves.
To get fraction's value divide the numerator by the denominator:
Value = 31 ÷ 40
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.
31 is a prime number, it cannot be factored into other prime factors;
In exponential notation:
40 = 2 × 2 × 2 × 5 = 23 × 5;
40 is a composite number;
* 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.
Calculate the greatest common factor, GCF:
Multiply all the common prime factors, by the lowest exponents.
But, the numerator and denominator have no common factors.
gcf (31; 23 × 5) = 1
The numerator and denominator of the fraction are coprime numbers (no common prime factors, GCF = 1).
The fraction cannot be reduced (simplified): irreducible fraction.
Fraction 31/40 is a positive proper fractions (numerator < denominator).
Rewrite the fraction:
As a decimal number:
31 ÷ 40 =
As a percentage:
'Percent (%)' means 'out of one hundred'.
p% = p 'out of one hundred'.
p% = p/100 = p ÷ 100.
Fraction 100/100 = 100% = 100 ÷ 100 = 1
Multiply a number by the fraction 100/100 and its value doesn't change:
0.775 × 100/100 =
In other words:
Calculate the fraction's value,
Multiply that number by 100,
Add the percent sign % to it.
The final answer:
:: written in three ways ::