A farmer plants seeds on \(\frac{2}{5}\) of his land in 5 \(\frac{1}{2}\) days. The farmer plants seeds on \(\_\) of his land per day.
Understand the Problem
The question is asking how much of the farmer's land is planted per day, given that he plants a specific fraction of his land in a certain amount of days. We need to determine the daily planting rate based on the information provided.
Answer
The farmer plants on $\frac{4}{55}$ of his land per day.
Answer for screen readers
The farmer plants on $\frac{4}{55}$ of his land per day.
Steps to Solve
- Convert Mixed Number to Improper Fraction
First, we convert the mixed number (5 \frac{1}{2}) days to an improper fraction.
$$ 5 \frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} $$
- Determine Daily Planting Rate
To find out how much the farmer plants per day, we divide the total land planted by the number of days.
The farmer plants $\frac{2}{5}$ of his land in $\frac{11}{2}$ days, so the daily rate is:
$$ \text{Daily Rate} = \frac{\frac{2}{5}}{\frac{11}{2}} = \frac{2}{5} \times \frac{2}{11} = \frac{4}{55} $$
- Identify the Correct Answer
Compare the daily planting rate calculated with the given options.
The farmer plants on $\frac{4}{55}$ of his land per day.
The farmer plants on $\frac{4}{55}$ of his land per day.
More Information
The answer indicates that for every day, the farmer manages to plant a small fraction of his total land. This calculation helps in understanding the daily productivity and can aid in planning accordingly.
Tips
- Forgetting to convert mixed numbers to improper fractions before performing calculations.
- Incorrectly dividing fractions; always remember to multiply by the reciprocal.
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