How to reduce (simplify) the common ordinary fraction 2,756/400 to the lowest terms, to the simplest equivalent form, irreducible, with the smallest possible numerator and denominator? The result written: As an improper fraction. As a mixed number. As a decimal number. As a percentage %
Reduce (simplify) the common ordinary fraction: 2,756/400
Detailed calculations and explanations, below
Common ordinary fractions. Introduction:
A common ordinary fraction is made up of two integer numbers and a fraction bar: 2,756/400
The integer number above the bar is called the numerator: 2,756
The integer number below the bar is called the denominator: 400
The fraction bar means that the numerator is dividing by the denominator.
To get the fraction's value divide the numerator by the denominator: The value = 2,756 ÷ 400
To completely 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.
Exponential notation. In the second example, 23 is the writing in exponential notation of the repeating multiplication: 2 × 2 × 2. 23 is called the power, 2 is the base, 3 is the exponent and 8 is the value of the power: 23 = 8.
The 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.
The prime factorizations:
Written with exponents: 2,756 = 2 × 2 × 13 × 53 = 22 × 13 × 53 2,756 is a composite number.
Written with exponents: 400 = 2 × 2 × 2 × 2 × 5 × 5 = 24 × 52 400 is a composite number.
Multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).
Reduce (simplify) the common ordinary fraction: 2,756/400
Divide the numerator and the denominator by their GCF:
2,756/400 =
(22 × 13 × 53)/(24 × 52) =
((22 × 13 × 53) ÷ 22) / ((24 × 52) ÷ 22) =
(13 × 53)/(22 × 52) =
689/100
The fraction is now reduced to the lowest terms equivalent.
The fraction is called irreducible and it has the smallest possible numerator and denominator.
* When it's 1, the denominator of the fraction can be omitted.
Why do we try to simplify fractions?
By reducing the values of the numerator and of the denominator of a fraction the calculations with that fraction are easier to do.
The fraction 689/100 is a positive improper fraction (the numerator > the denominator).
Rewrite the fraction
As a mixed number (also called a mixed fraction):
A mixed number: a whole number and a proper fraction, both having the same sign.
A proper fraction is a fraction in which the value of the numerator is less than the value of the denominator.
Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:
689 ÷ 100 = 6 and the remainder = 89 =>
689 = 6 × 100 + 89 =>
689/100 =
(6 × 100 + 89) / 100 =
6 + 89/100 =
6 89/100
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
6 89/100 =
6 + 89/100 =
6 + 89 ÷ 100 =
6.89
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.
6.89 =
6.89 × 100/100 =
689/100 =
689%
In other words:
(+) Calculate the fraction's value, (+) multiply that number by 100, and (+) add the percent sign % to it.
As a positive improper fraction: (the numerator > the denominator): 2,756/400 = 689/100
As a mixed number: (a whole number and a proper fraction having the same sign) 2,756/400 = 6 89/100
As a decimal number: 2,756/400 = 6.89
As a percentage: 2,756/400 = 689%
How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.
Reduce (simplify) common ordinary fractions, online calculator
Fractions reducing (simplifying) to the lowest terms, to the simplest equivalent form, irreducible. 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.