Question
4i) A farmer placed an order for \( \frac{127}{10} \) tons of fertilizer. He calculates that the corn fields will require \( \frac{61}{10} \) tons of it. How much fertilizer will the farmer have left for his other crops? (i) Write your answer as a fraction or as a whole or mixed number.
Ask by Paul Hill. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The farmer will have \( \frac{33}{5} \) tons or \( 6 \frac{3}{5} \) tons of fertilizer left for his other crops.
Solution
1. Write the total amount of fertilizer as a fraction: \( \frac{127}{10} \) tons.
2. Write the amount required for the corn fields as a fraction: \( \frac{61}{10} \) tons.
3. Subtract the corn field amount from the total amount:
\[
\frac{127}{10} - \frac{61}{10} = \frac{127 - 61}{10} = \frac{66}{10}.
\]
4. Simplify the fraction \( \frac{66}{10} \) by dividing both numerator and denominator by their greatest common divisor, which is 2:
\[
\frac{66 \div 2}{10 \div 2} = \frac{33}{5}.
\]
5. Optionally, convert the improper fraction to a mixed number:
\[
\frac{33}{5} = 6 \frac{3}{5}.
\]
The farmer will have \( \frac{33}{5} \) tons, or \( 6 \frac{3}{5} \) tons, of fertilizer left for his other crops.
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Beyond the Answer
To find out how much fertilizer the farmer will have left, we'll subtract the amount needed for the corn fields from the total amount ordered. The calculation is as follows: \[ \frac{127}{10} - \frac{61}{10} = \frac{127 - 61}{10} = \frac{66}{10} \] This fraction can be simplified to: \[ \frac{66}{10} = \frac{33}{5} = 6 \frac{3}{5} \] So, the farmer will have \( 6 \frac{3}{5} \) tons of fertilizer left for his other crops.