A farmer plants seeds on 2/5 of his land in 5 1/2 days. The farmer plants seeds on ____ of his land per day.
Understand the Problem
The question is asking us to determine how much land the farmer plants each day. It provides the amount of land planted and the time taken, requiring a calculation to find the daily planting rate.
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
- Identify Total Land and Time Taken
The farmer plants $\frac{2}{5}$ of his land in $5 \frac{1}{2}$ days. To work with improper fractions, convert $5 \frac{1}{2}$ to an improper fraction:
$$ 5 \frac{1}{2} = \frac{11}{2} $$
- Calculate the Planting Rate per Day
To find the rate at which the farmer plants his land per day, divide the land planted by the time taken:
$$ \text{Planting Rate} = \frac{\text{Land Planted}}{\text{Time Taken}} = \frac{\frac{2}{5}}{\frac{11}{2}} $$
- Simplify the Division of Fractions
To divide fractions, multiply by the reciprocal of the divisor:
$$ \text{Planting Rate} = \frac{2}{5} \times \frac{2}{11} = \frac{4}{55} $$
- Write the Result in the Blank
Now we can place the result into the blank:
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
This problem involves understanding how to convert mixed numbers to improper fractions and how to perform operations with fractions. Knowing these skills helps in various practical scenarios such as agriculture, finance, and cooking.
Tips
- Not converting mixed numbers to improper fractions before performing calculations, which can lead to incorrect results.
- Forgetting to multiply by the reciprocal when dividing fractions.
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