To determine if [tex]\(\frac{13}{7}\)[/tex] is a rational number, we need to examine whether it meets the definition of a rational number.
A rational number is any number that can be expressed in the form [tex]\(\frac{a}{b}\)[/tex], where [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers, and [tex]\(b \neq 0\)[/tex].
Let's analyze this step-by-step:
1. Form of the Number:
- [tex]\(\frac{13}{7}\)[/tex] is already in the form [tex]\(\frac{a}{b}\)[/tex].
2. Numerator (a):
- The numerator [tex]\(a\)[/tex] is 13.
- 13 is an integer.
3. Denominator (b):
- The denominator [tex]\(b\)[/tex] is 7.
- 7 is an integer.
- Importantly, 7 is not zero.
Since [tex]\(\frac{13}{7}\)[/tex] meets all the criteria of a rational number ([tex]\(a\)[/tex] and [tex]\(b\)[/tex] are integers and [tex]\(b \neq 0\)[/tex]), we can conclude that:
[tex]\(\frac{13}{7}\)[/tex] is indeed a rational number.
Therefore, [tex]\(\frac{13}{7} = \text{True}\)[/tex] as a rational number.
