Sure, let's walk through the calculations step-by-step based on the provided results and properties of zero and one.
### Property of Zero
1. [tex]\(\frac{-4}{7} + 0\)[/tex]
Adding zero to any number does not change its value.
Therefore, [tex]\(\frac{-4}{7} + 0 = -0.5714285714285714\)[/tex].
2. [tex]\(\frac{-2}{5} - 0\)[/tex]
Subtracting zero from any number does not change its value.
Therefore, [tex]\(\frac{-2}{5} - 0 = -0.4\)[/tex].
3. [tex]\(\frac{3}{8} \times 0\)[/tex]
Multiplying any number by zero results in zero.
Therefore, [tex]\(\frac{3}{8} \times 0 = 0.0\)[/tex].
4. [tex]\(\frac{1}{6} \div 0\)[/tex]
Division by zero is undefined, and thus this expression does not have a valid result.
### Property of One
5. [tex]\(1 + \frac{-5}{8}\)[/tex]
Adding an integer to a fraction, we simply combine the two values.
Therefore, [tex]\(1 + \frac{-5}{8} = 1 - \frac{5}{8} = \frac{8}{8} - \frac{5}{8} = \frac{3}{8} = 0.375\)[/tex].
6. [tex]\(\frac{-3}{4} - 1\)[/tex]
Subtracting an integer from a fraction, we convert it to a common denominator.
Therefore, [tex]\(\frac{-3}{4} - 1 = \frac{-3}{4} - \frac{4}{4} = \frac{-3-4}{4} = \frac{-7}{4} = -1.75\)[/tex].
7. [tex]\(\frac{-8}{11} \div 1\)[/tex]
Dividing any number by one does not change its value.
Therefore, [tex]\(\frac{-8}{11} \div 1 = -0.7272727272727273\)[/tex].
8. [tex]\(1 \times \frac{-8}{11}\)[/tex]
Multiplying any number by one does not change its value.
Therefore, [tex]\(1 \times \frac{-8}{11} = -0.7272727272727273\)[/tex].
9. [tex]\(0 \times \frac{3}{8}\)[/tex]
Multiplying any number by zero results in zero.
Therefore, [tex]\(0 \times \frac{3}{8} = 0.0\)[/tex].
These calculations demonstrate the basic properties of arithmetic operations involving zero and one. The results are consistent with these mathematical properties.
