Tool to reduce fractions in lowest terms. A Fraction in Lowest Terms (Irreducible Fraction) is a reduced fraction in which the numerator and the denominator are coprime (they do not share common factors)
Irreducible Fractions - dCode
Tag(s) : Arithmetics, Symbolic Computation
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Irreducible Fractions
Simplify Fractions in Lowest Terms
Decimal to Fraction in Lowest Terms Converter
Answers to Questions (FAQ)
What is a fraction in lowest terms? (Definition)
An irreducible fraction noted a/b or ab is one in which the denominator b (the number below the fraction bar, the divisor) is the smallest possible integer, while the numerator a (the dividend, the number above the fraction bar) must also be an integer.
Example: Any fraction can be written in many different ways while still retaining its value: 50100=510=24=12=0.5, but only 12 is an irreducible fraction.
Giving the result as an irreducible fraction is generally the preferred format for writing a fraction, as it is its simplest form. Mathematically, an irreducible fraction is a fraction whose numerator and denominator are coprime, that is, they have no common divisor other than 1. In other words, it is impossible to simplify it further.
How to make a fraction in lowest terms?
To simplify a fraction a/b:
— Identify the numbers a and b.
Example: The fraction 12/10 has a=12 as the numerator and b=10 as the denominator.
— Calculate the greatest common divisor (GCD) of the two numbers a and b.
Example: GCD(12,10)=2
— Divide the numerator a and the denominator b by their GCD values.
Example: Dividing the numerator gives 12/2=6 and for the denominator 10/2=5
— The irreducible fraction is therefore GCD(a)GCD(b)
Example: The fraction in the smallest form of 12/10 is 6/5
How do you know if a fraction is irreducible?
A fraction is irreducible if the GCD of its numerator and denominator is equal to 1.
Example: 713 is irreducible because GCD(7,13)=1
If GCD(a,b)>1 then the fraction is reducible.
Why make a fraction irreducible?
The irreducible fraction is the standard form expected in exercises, exams, or demonstrations. It allows you to:
— Present a result in its simplest form.
— Simplify calculations.
— Compare fractions more easily.
How to calculate and give the result under the lowest terms form?
Sometimes a fraction takes the form of a calculation. Calculate the numerator and denominator independently (addition, subtraction, multiplication, or division) before simplifying the fraction.
Example: (a+b)/(c−d)
dCode can perform this calculation automatically using the built-in formal calculator: enter the expression(s)/fraction(s) and the simplifier performs formal calculations to preserve any variables and return the simplest form of division (simplification the fraction into lowest term).
How to make a fraction from a decimal number?
If the number has a limited decimal development then it only needs to be multiplied by the right power of 10, then simplify the fraction and solve the equation.
Example: The number 0.14 is equivalent to 0.14/1, multiply by 10/10(=1) until having no comma: 0.14/1=1.4/10=14/100 then simplify 14/100=7/50
If the number has a non finite decimal expansion then it is necessary to locate the repeating portion of the number after the repeating decimal point.
Example: The number 0.166666666… where the 6 is repeated
If x is the decimal number, and n the size (number of digits) of the smallest repeated portion. To obtain a fraction, multiply x by 10n and then subtract x.
Example: x=0.1666666…, the smallest repeated portion is 6, which has a single digit so that n=1. Then compute 101×x=1.6666666… and 10x−x. 10x−x=9x=1.666666⋯−0.1666666⋯=1.5⟺9x=1.5⇒x=1.5/9=15/90=1/6 so 1/6=0.1666666…
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- Simplify Fractions in Lowest Terms
- Decimal to Fraction in Lowest Terms Converter
- What is a fraction in lowest terms? (Definition)
- How to make a fraction in lowest terms?
- How do you know if a fraction is irreducible?
- Why make a fraction irreducible?
- How to calculate and give the result under the lowest terms form?
- How to make a fraction from a decimal number?
