Question: A farmer has two fields to fertilize. The first field requires 8\frac{1}{2} tons of fertilizer and…

A farmer has two fields to fertilize. The first field requires 8\frac{1}{2} tons of fertilizer and the second one will need 9\frac{3}{4} tons. How much fertilizer will the farmer need altogether?

Solution

To find the total amount of fertilizer the farmer needs, we add the amounts for both fields. First field requires \(8 \frac{1}{2}\) tons: Convert the mixed number to an improper fraction: \[ 8 \frac{1}{2} = \frac{17}{2} \] Second field requires \(9 \frac{3}{4}\) tons: Convert the mixed number to an improper fraction: \[ 9 \frac{3}{4} = \frac{39}{4} \] Find a common denominator to add the fractions: The least common denominator of 2 and 4 is 4. Convert \(\frac{17}{2}\) to a fraction with a denominator of 4: \[ \frac{17}{2} = \frac{34}{4} \] Add the fractions: \[ \frac{34}{4} + \frac{39}{4} = \frac{73}{4} \] Convert the improper fraction back to a mixed number: \[ \frac{73}{4} = 18 \frac{1}{4} \] The farmer will need \(18 \frac{1}{4}\) tons of fertilizer altogether.