What is a fraction in which the greatest common factor of the numerator and the denominator is 1?

Question

What is this fraction:

A fraction in which the greatest common factor of the numerator and the denominator is 1?

Answer 1

This just means that the fraction has been reduced. For instance $4/6$ is not such a fraction, because the top and the bottom have gcf = 2, but $2/3$ is such a fraction.

Another way of saying it is that numerator and denominator are coprime.

Answer 2

A fraction in which the greatest common factor of the numerator and the denominator is 1 is known as a reduced, or simplified, fraction. $$\dfrac 68 \;\;\text{is not reduced (or not simplified) because} \;\dfrac 68 = \dfrac {\color{blue}{\bf 2}\cdot 3} {\color{blue}{\bf 2}\cdot 2\cdot 2}$$

$$\dfrac 34\;\;\text{ is a reduced, or simplified, fraction:}\;\dfrac {\color{blue}{\bf 1}\cdot 3}{\color{blue}{\bf 1}\cdot 2\cdot 2}$$

Answer 3

Quite often I have also heard this called a fraction in its lowest terms.