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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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.

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