To order and place the given fractions and whole numbers on a number line, we need to convert them into a consistent representation and understand their values:
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Convert the numbers to a common format:
- \( \frac{2}{3} \): This is approximately 0.67.
- \( -\frac{2}{3} \): This is approximately -0.67.
- \( 1 \): This is just 1.
- \( -1 \): This is just -1.
- \( \frac{1}{3} \): This is approximately 0.33.
- \( -\frac{1}{3} \): This is approximately -0.33.
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Order the numbers from least to greatest:
- Start from the left (the most negative) to the right (the most positive):
- \( -1 \): This is the leftmost point.
- \( -\frac{2}{3} \): This is greater than -1 and approximately -0.67.
- \( -\frac{1}{3} \): This is greater than \( -\frac{2}{3} \) and approximately -0.33.
- \( \frac{1}{3} \): This is greater than \( -\frac{1}{3} \) and approximately 0.33.
- \( \frac{2}{3} \): This is greater than \( \frac{1}{3} \) and approximately 0.67.
- \( 1 \): This is the rightmost point.
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Number Line Representation: Placing these values on a number line would look like this:
-1 -2/3 -1/3 0 1/3 2/3 1
<---|-------|---------|--------|--------|-------|--------|--->
Summary of the Order:
- From left to right, the order of the numbers is:
- \( -1 \)
- \( -\frac{2}{3} \)
- \( -\frac{1}{3} \)
- \( 0 \)
- \( \frac{1}{3} \)
- \( \frac{2}{3} \)
- \( 1 \)
This shows how each fraction and whole number fits on the number line in relation to each other, providing a clear visualization of their relative sizes.
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