Answer :
Let's address each part of the question in detail:
### Rational vs. Non-Rational Numbers
Rational numbers are those which can be expressed as the quotient or fraction [tex]\(\frac{p}{q}\)[/tex], where [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are integers and [tex]\( q \ne 0 \)[/tex].
1. [tex]\(\frac{8}{19}\)[/tex]: Circle it because [tex]\(\frac{8}{19}\)[/tex] is a rational number.
2. [tex]\(\frac{0}{7}\)[/tex]: Circle it because [tex]\(\frac{0}{7} = 0\)[/tex], which is a rational number.
3. [tex]\( \frac{32}{40} \)[/tex]: Circle it because [tex]\(\frac{32}{40} = 0.8\)[/tex], which is a rational number.
4. [tex]\(\frac{-8}{60}\)[/tex]: Circle it because [tex]\(\frac{-8}{60} = -0.13333333333333333\)[/tex], which is a rational number.
5. [tex]\(\frac{16}{0}\)[/tex]: Cross it because [tex]\(\frac{16}{0}\)[/tex] is undefined due to division by zero.
6. [tex]\(\frac{6}{12}\)[/tex]: Circle it because [tex]\(\frac{6}{12} = 0.5\)[/tex], which is a rational number.
7. [tex]\(\frac{8}{17}\)[/tex]: Circle it because [tex]\(\frac{8}{17}\)[/tex] is a rational number.
8. [tex]\(\frac{3}{4}\)[/tex]: Circle it because [tex]\(\frac{3}{4} = 0.75\)[/tex], which is a rational number.
9. [tex]\( \frac{1}{10} \)[/tex]: Circle it because [tex]\(\frac{1}{10} = 0.1\)[/tex], which is a rational number.
10. [tex]\( 3 \)[/tex]: Circle it because [tex]\(3\)[/tex] can be written as [tex]\(\frac{3}{1}\)[/tex], which is a rational number.
11. [tex]\(\frac{-2}{8} \)[/tex]: Circle it because [tex]\(\frac{-2}{8} = -0.25\)[/tex], which is a rational number.
12. [tex]\(\frac{9}{0}\)[/tex]: Cross it because [tex]\(\frac{9}{0}\)[/tex] is undefined due to division by zero.
13. [tex]\(\frac{0}{4}\)[/tex]: Circle it because [tex]\(\frac{0}{4} = 0\)[/tex], which is a rational number.
### Simplifying Rational Numbers
Express the rational numbers in simplest form:
1. [tex]\(\frac{32}{40} = 0.8\)[/tex]
2. [tex]\(\frac{-8}{60} = -0.13333333333333333\)[/tex]
3. [tex]\(\frac{6}{12} = 0.5\)[/tex]
4. [tex]\(\frac{-2}{8} = -0.25\)[/tex]
### Comparative Relations
Fill in the blanks using [tex]\(>\)[/tex] or [tex]\(<\)[/tex]:
1. [tex]\(\frac{-8}{19} < \frac{-7}{19}\)[/tex]
2. [tex]\(\frac{-13}{20} < \frac{3}{20}\)[/tex]
3. [tex]\(\frac{7}{8} > \frac{-3}{8}\)[/tex]
4. [tex]\(\frac{3}{4} > \frac{-2}{3}\)[/tex]
5. [tex]\(\frac{7}{8} < \frac{6}{7}\)[/tex]
### Additive Inverse
Find the additive inverse of the following numbers:
1. The additive inverse of [tex]\(\frac{3}{4}\)[/tex] is [tex]\(-\frac{3}{4} = -0.75\)[/tex].
2. The additive inverse of [tex]\(\frac{-2}{3}\)[/tex] is [tex]\(\frac{2}{3} = 0.6666666666666666\)[/tex].
### Multiplicative Inverse
Find the multiplicative inverse:
1. The multiplicative inverse of [tex]\(\frac{-6}{35}\)[/tex] is [tex]\(\frac{35}{-6} = -5.833333333333333\)[/tex].
### Undefined Values
Values that are undefined:
1. [tex]\(\frac{16}{0}\)[/tex]: undefined
2. [tex]\(\frac{9}{0}\)[/tex]: undefined
### Defined Zero Values
Values that are defined as zero:
1. [tex]\( \frac{0}{7} = 0 \)[/tex]
2. [tex]\( \frac{0}{4} = 0 \)[/tex]
All parts of the problem have been addressed in detail. If you have any more questions or need further explanation on any part of the solution, feel free to ask!
### Rational vs. Non-Rational Numbers
Rational numbers are those which can be expressed as the quotient or fraction [tex]\(\frac{p}{q}\)[/tex], where [tex]\( p \)[/tex] and [tex]\( q \)[/tex] are integers and [tex]\( q \ne 0 \)[/tex].
1. [tex]\(\frac{8}{19}\)[/tex]: Circle it because [tex]\(\frac{8}{19}\)[/tex] is a rational number.
2. [tex]\(\frac{0}{7}\)[/tex]: Circle it because [tex]\(\frac{0}{7} = 0\)[/tex], which is a rational number.
3. [tex]\( \frac{32}{40} \)[/tex]: Circle it because [tex]\(\frac{32}{40} = 0.8\)[/tex], which is a rational number.
4. [tex]\(\frac{-8}{60}\)[/tex]: Circle it because [tex]\(\frac{-8}{60} = -0.13333333333333333\)[/tex], which is a rational number.
5. [tex]\(\frac{16}{0}\)[/tex]: Cross it because [tex]\(\frac{16}{0}\)[/tex] is undefined due to division by zero.
6. [tex]\(\frac{6}{12}\)[/tex]: Circle it because [tex]\(\frac{6}{12} = 0.5\)[/tex], which is a rational number.
7. [tex]\(\frac{8}{17}\)[/tex]: Circle it because [tex]\(\frac{8}{17}\)[/tex] is a rational number.
8. [tex]\(\frac{3}{4}\)[/tex]: Circle it because [tex]\(\frac{3}{4} = 0.75\)[/tex], which is a rational number.
9. [tex]\( \frac{1}{10} \)[/tex]: Circle it because [tex]\(\frac{1}{10} = 0.1\)[/tex], which is a rational number.
10. [tex]\( 3 \)[/tex]: Circle it because [tex]\(3\)[/tex] can be written as [tex]\(\frac{3}{1}\)[/tex], which is a rational number.
11. [tex]\(\frac{-2}{8} \)[/tex]: Circle it because [tex]\(\frac{-2}{8} = -0.25\)[/tex], which is a rational number.
12. [tex]\(\frac{9}{0}\)[/tex]: Cross it because [tex]\(\frac{9}{0}\)[/tex] is undefined due to division by zero.
13. [tex]\(\frac{0}{4}\)[/tex]: Circle it because [tex]\(\frac{0}{4} = 0\)[/tex], which is a rational number.
### Simplifying Rational Numbers
Express the rational numbers in simplest form:
1. [tex]\(\frac{32}{40} = 0.8\)[/tex]
2. [tex]\(\frac{-8}{60} = -0.13333333333333333\)[/tex]
3. [tex]\(\frac{6}{12} = 0.5\)[/tex]
4. [tex]\(\frac{-2}{8} = -0.25\)[/tex]
### Comparative Relations
Fill in the blanks using [tex]\(>\)[/tex] or [tex]\(<\)[/tex]:
1. [tex]\(\frac{-8}{19} < \frac{-7}{19}\)[/tex]
2. [tex]\(\frac{-13}{20} < \frac{3}{20}\)[/tex]
3. [tex]\(\frac{7}{8} > \frac{-3}{8}\)[/tex]
4. [tex]\(\frac{3}{4} > \frac{-2}{3}\)[/tex]
5. [tex]\(\frac{7}{8} < \frac{6}{7}\)[/tex]
### Additive Inverse
Find the additive inverse of the following numbers:
1. The additive inverse of [tex]\(\frac{3}{4}\)[/tex] is [tex]\(-\frac{3}{4} = -0.75\)[/tex].
2. The additive inverse of [tex]\(\frac{-2}{3}\)[/tex] is [tex]\(\frac{2}{3} = 0.6666666666666666\)[/tex].
### Multiplicative Inverse
Find the multiplicative inverse:
1. The multiplicative inverse of [tex]\(\frac{-6}{35}\)[/tex] is [tex]\(\frac{35}{-6} = -5.833333333333333\)[/tex].
### Undefined Values
Values that are undefined:
1. [tex]\(\frac{16}{0}\)[/tex]: undefined
2. [tex]\(\frac{9}{0}\)[/tex]: undefined
### Defined Zero Values
Values that are defined as zero:
1. [tex]\( \frac{0}{7} = 0 \)[/tex]
2. [tex]\( \frac{0}{4} = 0 \)[/tex]
All parts of the problem have been addressed in detail. If you have any more questions or need further explanation on any part of the solution, feel free to ask!
