6th Grade Math Worksheets - Free Printable

Problem Analysis:

The task involves working with absolute values and opposites of numbers. Let's break it down step by step:

#### Part A: Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. Mathematically, the absolute value of a number \( x \) is denoted as \( |x| \) and is defined as:
- \( |x| = x \) if \( x \geq 0 \)
- \( |x| = -x \) if \( x < 0 \)

#### Part B: Opposite
The opposite of a number \( x \) is the number that, when added to \( x \), results in zero. Mathematically, the opposite of \( x \) is \( -x \).

Solution:

#### Part A: Absolute Value
We need to find the absolute value of each given number.

1. Given Example:
- Number: \( -5 \)
- Absolute Value: \( |-5| = 5 \)

2. Other Examples:
- Number: \( 3 \)
- Absolute Value: \( |3| = 3 \)
- Number: \( -9 \)
- Absolute Value: \( |-9| = 9 \)
- Number: \( 4 \)
- Absolute Value: \( |4| = 4 \)
- Number: \( -7 \)
- Absolute Value: \( |-7| = 7 \)
- Number: \( 8 \)
- Absolute Value: \( |8| = 8 \)
- Number: \( -6 \)
- Absolute Value: \( |-6| = 6 \)
- Number: \( 1 \)
- Absolute Value: \( |1| = 1 \)
- Number: \( -10 \)
- Absolute Value: \( |-10| = 10 \)
- Number: \( 0 \)
- Absolute Value: \( |0| = 0 \)

#### Part B: Opposite
We need to find the opposite of each given number.

1. Given Example:
- Number: \( -5 \)
- Opposite: \( -(-5) = 5 \)

2. Other Examples:
- Number: \( 3 \)
- Opposite: \( -(3) = -3 \)
- Number: \( -9 \)
- Opposite: \( -(-9) = 9 \)
- Number: \( 4 \)
- Opposite: \( -(4) = -4 \)
- Number: \( -7 \)
- Opposite: \( -(-7) = 7 \)
- Number: \( 8 \)
- Opposite: \( -(8) = -8 \)
- Number: \( -6 \)
- Opposite: \( -(-6) = 6 \)
- Number: \( 1 \)
- Opposite: \( -(1) = -1 \)
- Number: \( -10 \)
- Opposite: \( -(-10) = 10 \)
- Number: \( 0 \)
- Opposite: \( -(0) = 0 \)

Final Answer:

#### Part A: Absolute Values
\[
\begin{array}{c|c}
\text{NUMBER} & \text{ABSOLUTE VALUE} \\
\hline
3 & 3 \\
-9 & 9 \\
4 & 4 \\
-7 & 7 \\
8 & 8 \\
-6 & 6 \\
1 & 1 \\
-10 & 10 \\
0 & 0 \\
\end{array}
\]

#### Part B: Opposites
\[
\begin{array}{c|c}
\text{NUMBER} & \text{OPPOSITE} \\
\hline
3 & -3 \\
-9 & 9 \\
4 & -4 \\
-7 & 7 \\
8 & -8 \\
-6 & 6 \\
1 & -1 \\
-10 & 10 \\
0 & 0 \\
\end{array}
\]

Boxed Final Answer:

\[
\boxed{
\begin{array}{c|c|c}
\text{NUMBER} & \text{ABSOLUTE VALUE} & \text{OPPOSITE} \\
\hline
3 & 3 & -3 \\
-9 & 9 & 9 \\
4 & 4 & -4 \\
-7 & 7 & 7 \\
8 & 8 & -8 \\
-6 & 6 & 6 \\
1 & 1 & -1 \\
-10 & 10 & 10 \\
0 & 0 & 0 \\
\end{array}
}
\]