Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Sure, let's fill in the table with detailed steps for each operation.
### Table-1
#### Row 1
1. Rational Numbers: [tex]\( \frac{-1}{2}, \frac{3}{4} \)[/tex]
2. Operation: +
3. Result Calculation:
[tex]\[ \frac{-1}{2} + \frac{3}{4} = \frac{-2 + 3}{4} = \frac{1}{4} \][/tex]
4. Closure Property: Rational number (since the result [tex]\( \frac{1}{4} \)[/tex] is a rational number)
5. Commutative Property:
[tex]\[ \frac{-1}{2} + \frac{3}{4} = \frac{3}{4} + \frac{-1}{2} \][/tex]
(Addition is commutative)
#### Row 2
1. Rational Numbers: [tex]\( \frac{-3}{8}, \frac{2}{3} \)[/tex]
2. Operation: -
3. Result Calculation:
[tex]\[ \frac{-3}{8} - \frac{2}{3} = \frac{-3 \times 3 - 2 \times 8}{8 \times 3}= \frac{-9 -16}{24} = \frac{-25}{24} \][/tex]
4. Closure Property: Rational number (since the result [tex]\(\frac{-25}{24}\)[/tex] is a rational number)
5. Commutative Property:
[tex]\[ \frac{-3}{8} - \frac{2}{3} \neq \frac{2}{3} - \frac{-3}{8} \][/tex]
(Subtraction is not commutative)
#### Row 3
1. Rational Numbers: [tex]\( \frac{4}{5}, \frac{-1}{5} \)[/tex]
2. Operation: +
3. Result Calculation:
[tex]\[ \frac{4}{5} + \frac{-1}{5} = \frac{4 - 1}{5} = \frac{3}{5} \][/tex]
4. Closure Property: Rational number (since the result [tex]\(\frac{3}{5}\)[/tex] is a rational number)
5. Commutative Property:
[tex]\[ \frac{4}{5} + \frac{-1}{5} = \frac{-1}{5} + \frac{4}{5} \][/tex]
(Addition is commutative)
#### Row 4
1. Rational Numbers: [tex]\( \frac{8}{9}, \frac{-5}{7} \)[/tex]
2. Operation: [tex]\(\times\)[/tex]
3. Result Calculation:
[tex]\[ \frac{8}{9} \times \frac{-5}{7} = \frac{8 \times -5}{9 \times 7} = \frac{-40}{63} \][/tex]
4. Closure Property: Rational number (since the result [tex]\(\frac{-40}{63}\)[/tex] is a rational number)
5. Commutative Property:
[tex]\[ \frac{8}{9} \times \frac{-5}{7} = \frac{-5}{7} \times \frac{8}{9} \][/tex]
(Multiplication is commutative)
### Final Table
\begin{tabular}{|c|c|c|c|c|c|}
\hline \multicolumn{2}{|c|}{ Rational Numbers } & Operation & Result & Closure Property & Commutative Property \\
\hline[tex]$\frac{-1}{2}$[/tex] & [tex]$\frac{3}{4}$[/tex] & + & [tex]$\frac{1}{4}$[/tex] & Rational number & Yes \\
\hline[tex]$\frac{-3}{8}$[/tex] & [tex]$\frac{2}{3}$[/tex] & - & [tex]$\frac{-25}{24}$[/tex] & Rational number & No \\
\hline[tex]$\frac{4}{5}$[/tex] & [tex]$\frac{-1}{5}$[/tex] & + & [tex]$\frac{3}{5}$[/tex] & Rational number & Yes \\
\hline[tex]$\frac{8}{9}$[/tex] & [tex]$\frac{-5}{7}$[/tex] & [tex]\(\times\)[/tex] & [tex]$\frac{-40}{63}$[/tex] & Rational number & Yes \\
\hline
\end{tabular}
This table provides a clear overview of the operations performed on the given rational numbers, the results, and examines their closure and commutative properties.
### Table-1
#### Row 1
1. Rational Numbers: [tex]\( \frac{-1}{2}, \frac{3}{4} \)[/tex]
2. Operation: +
3. Result Calculation:
[tex]\[ \frac{-1}{2} + \frac{3}{4} = \frac{-2 + 3}{4} = \frac{1}{4} \][/tex]
4. Closure Property: Rational number (since the result [tex]\( \frac{1}{4} \)[/tex] is a rational number)
5. Commutative Property:
[tex]\[ \frac{-1}{2} + \frac{3}{4} = \frac{3}{4} + \frac{-1}{2} \][/tex]
(Addition is commutative)
#### Row 2
1. Rational Numbers: [tex]\( \frac{-3}{8}, \frac{2}{3} \)[/tex]
2. Operation: -
3. Result Calculation:
[tex]\[ \frac{-3}{8} - \frac{2}{3} = \frac{-3 \times 3 - 2 \times 8}{8 \times 3}= \frac{-9 -16}{24} = \frac{-25}{24} \][/tex]
4. Closure Property: Rational number (since the result [tex]\(\frac{-25}{24}\)[/tex] is a rational number)
5. Commutative Property:
[tex]\[ \frac{-3}{8} - \frac{2}{3} \neq \frac{2}{3} - \frac{-3}{8} \][/tex]
(Subtraction is not commutative)
#### Row 3
1. Rational Numbers: [tex]\( \frac{4}{5}, \frac{-1}{5} \)[/tex]
2. Operation: +
3. Result Calculation:
[tex]\[ \frac{4}{5} + \frac{-1}{5} = \frac{4 - 1}{5} = \frac{3}{5} \][/tex]
4. Closure Property: Rational number (since the result [tex]\(\frac{3}{5}\)[/tex] is a rational number)
5. Commutative Property:
[tex]\[ \frac{4}{5} + \frac{-1}{5} = \frac{-1}{5} + \frac{4}{5} \][/tex]
(Addition is commutative)
#### Row 4
1. Rational Numbers: [tex]\( \frac{8}{9}, \frac{-5}{7} \)[/tex]
2. Operation: [tex]\(\times\)[/tex]
3. Result Calculation:
[tex]\[ \frac{8}{9} \times \frac{-5}{7} = \frac{8 \times -5}{9 \times 7} = \frac{-40}{63} \][/tex]
4. Closure Property: Rational number (since the result [tex]\(\frac{-40}{63}\)[/tex] is a rational number)
5. Commutative Property:
[tex]\[ \frac{8}{9} \times \frac{-5}{7} = \frac{-5}{7} \times \frac{8}{9} \][/tex]
(Multiplication is commutative)
### Final Table
\begin{tabular}{|c|c|c|c|c|c|}
\hline \multicolumn{2}{|c|}{ Rational Numbers } & Operation & Result & Closure Property & Commutative Property \\
\hline[tex]$\frac{-1}{2}$[/tex] & [tex]$\frac{3}{4}$[/tex] & + & [tex]$\frac{1}{4}$[/tex] & Rational number & Yes \\
\hline[tex]$\frac{-3}{8}$[/tex] & [tex]$\frac{2}{3}$[/tex] & - & [tex]$\frac{-25}{24}$[/tex] & Rational number & No \\
\hline[tex]$\frac{4}{5}$[/tex] & [tex]$\frac{-1}{5}$[/tex] & + & [tex]$\frac{3}{5}$[/tex] & Rational number & Yes \\
\hline[tex]$\frac{8}{9}$[/tex] & [tex]$\frac{-5}{7}$[/tex] & [tex]\(\times\)[/tex] & [tex]$\frac{-40}{63}$[/tex] & Rational number & Yes \\
\hline
\end{tabular}
This table provides a clear overview of the operations performed on the given rational numbers, the results, and examines their closure and commutative properties.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
