Using a number line to order integers is a visual and straightforward method: integers to the left are always smaller than integers to the right.
Here's a breakdown of how to do it:
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Visualize the Number Line: Imagine a horizontal line with zero in the middle. Positive integers are to the right of zero, and negative integers are to the left.
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Locate the Integers: Find the positions of the integers you want to order on the number line.
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Compare Positions:
- An integer further to the right is greater than an integer further to the left.
- An integer further to the left is smaller than an integer further to the right.
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Zero as the Reference Point: All negative integers are less than zero, and all positive integers are greater than zero.
Key Principles:
- Negative Integers: The further a negative integer is from zero (to the left), the smaller its value. For example, -5 is smaller than -2.
- Positive Integers: The further a positive integer is from zero (to the right), the greater its value. For example, 5 is greater than 2.
Examples:
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Ordering -3, 1, -5, 0, 2:
On the number line, the order from left to right (smallest to largest) would be: -5, -3, 0, 1, 2.
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Comparing -4 and -1:
-4 is to the left of -1 on the number line. Therefore, -4 is smaller than -1 (-4 < -1).
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Comparing 3 and -2:
3 is to the right of -2 on the number line. Therefore, 3 is greater than -2 (3 > -2).
In Summary: A number line provides a visual representation that makes ordering integers very intuitive. Integers increase in value as you move from left to right along the number line. The further left an integer is, the smaller it is, and the further right it is, the larger it is.
