# Adjective for a fraction that can't be represented in a simpler way

7/21 can still be represented as 1/3,

3/12 can still be represented as 1/4,

2/26 can still be represented as 1/13, but

9/13 can not be represented in any simpler way.

So, if I ask a student to find among these 4 fractions the one that cannot be represented in a simpler way, what adjective should I use in this question:

Which one of the following options is a ________________ fraction?

Should it be:

1. simplest ?

2. simple ?

3. non-simplified ?

4. basic ?

5. most basic ?

6. natural ?

7. final ?

8. fundamental ?

9. ?

• Which is "not a reducible fraction", or "an irreducible fraction". Commented Nov 7, 2020 at 3:34
• Wikipedia offers some common synonyms: en.wikipedia.org/wiki/Irreducible_fraction
– d_b
Commented Nov 7, 2020 at 3:38
• @JackO'Flaherty - This is the Answer! Commented Nov 7, 2020 at 3:41

Mathematicians use the term reduced. Lexico has

reduce
VERB

3.2 Convert a fraction to (the form with the lowest terms).

This is supported by the math site Wolfram

Reduced Fraction

A fraction a/b written in lowest terms, i.e., by dividing numerator and denominator through by their greatest common divisor (a,b). For example, 2/3 is the reduced fraction of 8/12.

So the sentence becomes

Which one of the following options is a reduced fraction?

I am not sure there is a word that will clearly convey what you want to say. Many of those words would technically work, since the "simplest" could potentially refer to the fraction that is already "fully simplified," and so on. If I were you, however, I would rephrase the question slightly to increase clarity. Ask something like:

Which of the following fractions is already in its simplest form?

Or:

Which of these fractions cannot be further reduced?

It is a “fraction in lowest terms” or a “fraction in least terms.” The numerator and denominator share no prime factors. Shared prime factors can be cancelled.