Math 2.0

Number theory Theorem

Fraction in lowest terms

Builds on Rational numbersIntegers

Statement

Let qq be a rational number. Then there is exactly one pair of integers aa and bb with b>0b > 0, gcd⁡(a,b)=1\gcd(a, b) = 1 and q=a/bq = a / b.

Remarks

The fraction a/ba / b is the irreducible fraction, or the fraction in lowest terms, of qq. To find it from any fraction c/dc / d with d≠0d \neq 0, divide cc and dd by ±gcd⁡(c,d)\pm \gcd(c, d), with the sign that makes the denominator positive. For example, −6/−4-6 / -4 has lowest terms 3/23 / 2.

Reading path

To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Integers, object, no evidence levelIntegersobjectRational numbers, object, no evidence levelRational numbersobjectFraction in lowest terms, statement, no evidence levelFraction in lowest te…statement
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  1. Integers object
  2. Rational numbers object
  3. Fraction in lowest terms statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Irreducible_fraction, Uniqueness
  2. Web https://en.wikipedia.org/wiki/Rational_number, Irreducible fraction
About this page
Tag0R64A2CVN4
URIm2://0R64A2CVN4
Aliasesirreducible-fraction, reduced-fraction
Kindstatement, theorem
WritingW0 stub
MSC11A05
StatusThis copy of the site has no build data. Run m2 status 0R64A2CVN4.
UsesRational numbers, Integers

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