Math Problem Statement
Solution
The worksheet you’ve uploaded involves understanding integers through opposites, absolute values, number lines, and comparisons. Let's go through the parts of the worksheet one by one.
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Opposites of integers:
- The opposite of is .
- The opposite of is .
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Absolute values:
- The absolute value of is , written as .
- The absolute value of is also , written as .
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Number line:
- You need to plot and on the number line, with to the right of and to the left of .
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Comparisons:
- Use and to compare the numbers. Two examples:
- Use and to compare the numbers. Two examples:
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Real-life situation for integers:
- You could represent and in a real-life scenario. For example:
- could represent gaining $1.
- could represent losing $1.
- You could represent and in a real-life scenario. For example:
Would you like further explanations or help with another part of the worksheet?
Here are five related questions to extend this topic:
- What is the opposite of any positive integer?
- How do you represent the absolute value of on a number line?
- Can you find two more examples of integer comparisons using and ?
- How does temperature relate to positive and negative integers?
- How would you represent the opposite of zero?
Tip: When comparing integers, remember that any positive integer is always greater than any negative integer!
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Math Problem Analysis
Mathematical Concepts
Integers
Opposites of integers
Absolute value
Number line
Comparing integers
Formulas
Opposite of a number: If x is a number, its opposite is -x.
Absolute value: |x| represents the non-negative value of x.
Theorems
Properties of Opposites: The opposite of a positive integer is a negative integer and vice versa.
Absolute Value Theorem: The absolute value of any number is its distance from zero on the number line.
Suitable Grade Level
Grades 6-8
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