To find out how much of the report is left to write, we first need to calculate how much of the report Maria, Mike, and Patti have already written together.
- Maria has written \( \frac{1}{10} \).
- Mike has written \( \frac{1}{4} = \frac{2.5}{10} \) (or \( \frac{5}{20} \)).
- Patti has written \( \frac{1}{8} = \frac{1.25}{10} \) (or \( \frac{2.5}{20} \)).
Now, let's convert all fractions to a common denominator to add them easily. The least common multiple of 10, 4, and 8 is 40.
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Maria's contribution: \( \frac{1}{10} = \frac{4}{40} \)
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Mike's contribution: \( \frac{1}{4} = \frac{10}{40} \)
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Patti's contribution: \( \frac{1}{8} = \frac{5}{40} \)
Now, let's add these fractions together: \[ \frac{4}{40} + \frac{10}{40} + \frac{5}{40} = \frac{19}{40} \]
Next, we need to determine how much of the report is left to write. Since the total report can be represented as 1 (or \( \frac{40}{40} \)), we subtract the amount they've written from 1: \[ \text{Amount left} = 1 - \frac{19}{40} = \frac{40}{40} - \frac{19}{40} = \frac{21}{40} \]
Next, we compare \( \frac{21}{40} \) to \( \frac{1}{2} \):
- \( \frac{1}{2} = \frac{20}{40} \)
Now, since \( \frac{21}{40} > \frac{20}{40} \), it shows that they have more than \( \frac{1}{2} \) of their report left to write.
So the answer is:
They have more than \( \frac{1}{2} \) of their report left to write.