📄 6th Grade Math: Integers and Absolute Value Worksheet
📌 1. True / False
1. All whole numbers are integers.
2. The absolute value of a number is always positive.
3. On a number line, -7 is to the left of -3.
4. Zero is considered a positive integer.
5. The opposite of 10 is -10.
✏️ 2. Fill in the Blanks
1. Numbers less than zero are called integers.
2. The of a number is its distance from zero on a number line.
3. The opposite of -12 is .
4. On a horizontal number line, numbers increase as you move to the .
5. An integer is a number that can be positive, negative, or zero.
🔗 3. Matching
« A whole number that can be positive, negative, or zero.
« The distance of a number from zero on a number line, always non-negative.
« An integer that is less than zero.
« An integer that is greater than zero.
« A line on which numbers are marked at regular intervals.
✍️ 4. Short Answer Questions
1. What is the absolute value of -25?
💡 Suggested Answer: The absolute value of -25 is 25. \(|-25| = 25\).
2. Order the following integers from least to greatest: \(0, -5, 3, -1, 4\).
💡 Suggested Answer: The integers ordered from least to greatest are: \(-5, -1, 0, 3, 4\).
🎯 5. Multiple Choice
1. Which of the following numbers is an integer?
2. Which statement about absolute value is true?
3. A diver is 50 feet below sea level. How would you represent this depth as an integer?
📝 6. Open-Ended Questions
1. Explain what an integer is and provide three examples of integers that are not whole numbers.
💡 Solution Steps:
Step 1: Define an integer.\
An integer is a whole number that can be positive, negative, or zero. It includes all the counting numbers \((1, 2, 3, ...)\), their negative counterparts \((-1, -2, -3, ...)\), and zero.\
Step 2: Identify integers that are not whole numbers.\
Whole numbers are \(0, 1, 2, 3, ...\). Integers that are not whole numbers must therefore be negative integers.\
Step 3: Provide three examples.\
Examples of integers that are not whole numbers include \(-1, -10, -100\) (or any other negative integer).
2. Compare \(-15\) and \(-8\) using \(<\), \(>\), or \(=\). Explain your reasoning using the concept of a number line.
💡 Solution Steps:
Step 1: Place the numbers on a mental number line.\
Imagine a horizontal number line. Zero is in the middle, positive numbers are to the right, and negative numbers are to the left.\
Step 2: Locate \(-15\) and \(-8\) on the number line.\
Both \(-15\) and \(-8\) are negative integers, so they are to the left of zero. \(-15\) is further to the left of zero than \(-8\).\
Step 3: Determine the relationship.\
On a number line, numbers increase in value as you move from left to right. Since \(-15\) is to the left of \(-8\), \(-15\) is less than \(-8\).\
Step 4: Write the comparison.\
Therefore, \(-15 < -8\).
3. The temperature in a town was \(3^{\circ}\text{C}\) at noon. By midnight, the temperature dropped by \(10^{\circ}\text{C}\). What was the temperature at midnight? What is the absolute value of the midnight temperature?
💡 Solution Steps:
Step 1: Determine the temperature change.\
The starting temperature was \(3^{\circ}\text{C}\). The temperature dropped by \(10^{\circ}\text{C}\), which means we subtract \(10\) from the initial temperature.\
Step 2: Calculate the midnight temperature.\
Midnight temperature \(= 3^{\circ}\text{C} - 10^{\circ}\text{C} = -7^{\circ}\text{C}\).\
Step 3: Find the absolute value of the midnight temperature.\
The midnight temperature is \(-7^{\circ}\text{C}\). The absolute value of \(-7\) is its distance from zero, which is \(7\).\
Step 4: State the final answers.\
The temperature at midnight was \(-7^{\circ}\text{C}\). The absolute value of the midnight temperature is \(7^{\circ}\text{C}\).
Name Surname: .................................. Date: .... / .... / 202...
Integers and Absolute Value Worksheet
SCORE
A. True (T) / False (F)
( .... )
All whole numbers are integers.
( .... )
The absolute value of a number is always positive.
( .... )
On a number line, -7 is to the left of -3.
( .... )
Zero is considered a positive integer.
( .... )
The opposite of 10 is -10.
B. Fill in the Blanks
1)
Numbers less than zero are called .................... integers.
2)
The .................... of a number is its distance from zero on a number line.
3)
The opposite of -12 is .....................
4)
On a horizontal number line, numbers increase as you move to the .....................
5)
An integer is a .................... number that can be positive, negative, or zero.
C. Matching Concepts
( .... )
A whole number that can be positive, negative, or zero.
- Number Line
( .... )
The distance of a number from zero on a number line, always non-negative.
- Negative Integer
( .... )
An integer that is less than zero.
- Integer
( .... )
An integer that is greater than zero.
- Positive Integer
( .... )
A line on which numbers are marked at regular intervals.
- Absolute Value
D. Short Answer Questions
1)
What is the absolute value of -25?
2)
Order the following integers from least to greatest: \(0, -5, 3, -1, 4\).
A diver is 50 feet below sea level. How would you represent this depth as an integer?
A) \(50\)B) \(-50\)C) \(|50|\)D) \(|-50|\)
F. Open-Ended Questions
1)
Explain what an integer is and provide three examples of integers that are not whole numbers.
2)
Compare \(-15\) and \(-8\) using \(<\), \(>\), or \(=\). Explain your reasoning using the concept of a number line.
3)
The temperature in a town was \(3^{\circ}\text{C}\) at noon. By midnight, the temperature dropped by \(10^{\circ}\text{C}\). What was the temperature at midnight? What is the absolute value of the midnight temperature?