Let's evaluate Marissa's steps to identify any errors she made while ordering the numbers from least to greatest.
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Writing each decimal as a fraction:
- \(1.4\) can be written as \(\frac{14}{10}\), which simplifies to \(\frac{7}{5}\).
- \(0.2\) can be written as \(\frac{2}{10}\), which simplifies to \(\frac{1}{5}\).
- The negative fractions are already in fraction form: \(-\frac{1}{6}\), \(-\frac{1}{3}\), and \(\frac{2}{3}\).
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Writing every fraction with a common denominator of 18:
- \(-\frac{1}{6} = -\frac{3}{18}\)
- \(-\frac{1}{3} = -\frac{6}{18}\)
- \(\frac{1}{5} = \frac{3.6}{18}\) (usually results in a non-integer, which causes confusion here; it should be approximated instead)
- \(\frac{7}{5} = \frac{25.2}{18}\) (same reasoning as above)
- \(\frac{2}{3} = \frac{12}{18}\)
Since she is using a common denominator here, she should correctly convert all these values to fractions with a common denominator rather than leaving them as they originally were.
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Plotting the numbers on the number line:
- Marissa should plot accurate values based on their decimal or fraction representation.
- The correct order of the values should be accounted, focusing on more accurate decimal representations than relying on fractional comparisons inadequately adjusted (i.e., those additional non-integers might likely lead to incorrect placements).
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Listing the numbers from left to right as they are plotted on the number line:
- If she listed them correctly considering where each number belongs on a number line when plotted accurately, there should not be an issue.
Error Identification:
- Marissa should have only plotted the fractions on the number line.: This is misleading; plotting decimals or fractions equally works if the values are properly converted.
- Marissa should have used 30 as the common denominator.: This is incorrect; while 30 could work, she used 18 and should just ensure proper listings regardless.
- Marissa should have listed the numbers from right to left after she plotted them on the number line.: This is wrong; it should be from left to right as numbers progress along the number line.
Conclusively analyzing the steps, Marissa made an adjustment error in the calculations for the fractions (regarding the common denominator) and should maintain clarity whether employing decimals for representation or fractions assured she ensures they're plotted rightly. She did not make the listed errors as proposed in the choices presented, emphasizing that her potential numerical calculation led to equivocal influences rather than strictly following a specific pre-set rule within bounds.
The statement about "common denominator of 30," and correct left-to-right listing, rather invalidates the approach presented if weighed contextually with consistent arithmetic principles.