Sure, let’s work through the process step-by-step and classify each of the expressions given.
### Step-by-Step Simplification and Classification:
1. Expression: [tex]\( -(8 \div 2) \)[/tex]
- Simplification: [tex]\( 8 \div 2 = 4 \)[/tex]
- Negating it: [tex]\( -4 \)[/tex]
- Classification: Negative number
2. Expression: [tex]\( -5 \times (-4) \)[/tex]
- Simplification: Product of two negative numbers [tex]\( -5 \times -4 = 20 \)[/tex]
- Classification: Positive number
3. Expression: [tex]\( 6 \div (-3) \)[/tex]
- Simplification: [tex]\( 6 \div -3 = -2 \)[/tex]
- Classification: Negative number
4. Expression: [tex]\( -10 \div (-10) \)[/tex]
- Simplification: Division of two negative numbers [tex]\( -10 \div -10 = 1 \)[/tex]
- Classification: Positive number
5. Expression: [tex]\( -25 \times (-4) \)[/tex]
- Simplification: Product of two negative numbers [tex]\( -25 \times -4 = 100 \)[/tex]
- Classification: Positive number
6. Expression: [tex]\( -21 \div 7 \)[/tex]
- Simplification: [tex]\( -21 \div 7 = -3 \)[/tex]
- Classification: Negative number
### Categorized Results:
[tex]\[
\begin{array}{c}
-(8 \div 2) = -4 \\
6 \div(-3) = -2 \\
-21 \div 7 = -3 \\
\end{array}
\][/tex]
[tex]\[
\begin{array}{c}
-5 \times(-4) = 20 \\
-10 \div(-10) = 1 \\
-25 \times(-4) = 100 \\
\end{array}
\][/tex]
### Final Classification in a Table:
[tex]\[
\begin{array}{|l|l|}
\hline
\text{A negative number} & \text{A positive number} \\
\hline
-(8 \div 2) & -5 \times (-4) \\
6 \div (-3) & -10 \div (-10) \\
-21 \div 7 & -25 \times (-4) \\
\hline
\end{array}
\][/tex]
