Certainly! Let's go through each of the given fractions and determine whether they are rational numbers or not. Remember, a rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
1. [tex]\(\frac{8}{19}\)[/tex]
- Rational: The fraction [tex]\(\frac{8}{19}\)[/tex] is a rational number because both the numerator (8) and the denominator (19) are integers, and the denominator is not zero. So, we circle this number.
2. [tex]\(\frac{0}{7}\)[/tex]
- Rational: The fraction [tex]\(\frac{0}{7}\)[/tex] is a rational number because both the numerator (0) and the denominator (7) are integers, and the denominator is not zero. Any fraction with a zero numerator is still rational. So, we circle this number.
3. [tex]\(\frac{7}{9}\)[/tex]
- Rational: The fraction [tex]\(\frac{7}{9}\)[/tex] is a rational number because both the numerator (7) and the denominator (9) are integers, and the denominator is not zero. So, we circle this number.
4. [tex]\(\frac{16}{0}\)[/tex]
- Not Rational: The fraction [tex]\(\frac{16}{0}\)[/tex] is not a rational number because division by zero is undefined. The denominator is zero, making this fraction invalid in the set of rational numbers. So, we cross this number.
5. [tex]\(\frac{6}{12}\)[/tex]
- Rational: The fraction [tex]\(\frac{6}{12}\)[/tex] is a rational number because both the numerator (6) and the denominator (12) are integers, and the denominator is not zero. So, we circle this number.
6. [tex]\(\frac{8}{17}\)[/tex]
- Rational: The fraction [tex]\(\frac{8}{17}\)[/tex] is a rational number because both the numerator (8) and the denominator (17) are integers, and the denominator is not zero. So, we circle this number.
So, the rational numbers are:
1. [tex]\(\frac{8}{19}\)[/tex]
2. [tex]\(\frac{0}{7}\)[/tex]
3. [tex]\(\frac{7}{9}\)[/tex]
5. [tex]\(\frac{6}{12}\)[/tex]
6. [tex]\(\frac{8}{17}\)[/tex]
And the non-rational number is:
1. [tex]\(\frac{16}{0}\)[/tex]
