Reduce the Common Fraction - 31/10, Simplify It to the Lowest Terms, the Simplest Equivalent Form, Irreducible. Online Calculator
After reducing - 31/10, the simplified fraction is converted and written as a decimal number, as a percentage and as a mixed number
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.
The prime factorizations:
31 is a prime number, it cannot be factored (into other prime factors).
10 = 2 × 5
10 is a composite number.
Prime number: a positive integer that is dividing evenly (without a remainder) only by itself and 1. A prime number has only two factors. Composite number: a positive integer that has at least one factor (divisor) other than 1 and itself.
2. Multiply all the common prime factors:
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).
But the numerator and the denominator have no common prime factors.
GCF (31; 2 × 5) = 1
Reduce (simplify) the common ordinary fraction: - 31/10
The fraction cannot be reduced (simplified)
The GCF = 1, the numerator and denominator of the fraction are coprime numbers (they are prime to each other, they have no common prime factors).
The fraction is called irreducible and it has the smallest possible numerator and denominator.
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 becoming easier to do.
The fraction - 31/10 is a negative 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:
- 31 ÷ 10 = - 3 and the remainder = - 1 ⇒
- 31 = - 3 × 10 - 1 ⇒
- 31/10 =
( - 3 × 10 - 1) / 10 =
- 3 - 1/10 =
- 3 1/10
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 3 1/10 =
- 3 - 1/10 =
- 3 - 1 ÷ 10 =
- 3.1
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.
- 3.1 =
- 3.1 × 100/100 =
- 310/100 =
- 310%
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 four ways
As a negative improper fraction:
(|the numerator| > |the denominator|):
- 31/10 = - 31/10
As a mixed number:
(a whole number and a proper fraction having the same sign)
- 31/10 = - 3 1/10
As a decimal number:
- 31/10 = - 3.1
As a percentage:
- 31/10 = - 310%
More operations like this:
How are the numbers written: comma ',' used as a thousands separator; point '.' as a decimal separator; numbers rounded off to max. 12 decimals (if the case). Used symbols: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.
Reduce (simplify) common fractions, online calculator