To determine how many pounds of apples Michael needs to make \( \frac{3}{4} \) of a batch of applesauce, we first need to find out how much apple he needs for \( \frac{3}{4} \) of 2.5 pounds.
First, convert 2.5 pounds into a fraction: \[ 2.5 = \frac{5}{2} \] Now, multiply \( \frac{5}{2} \) by \( \frac{3}{4} \): \[ \frac{3}{4} \times \frac{5}{2} = \frac{3 \times 5}{4 \times 2} = \frac{15}{8} \]
Next, we convert \( \frac{15}{8} \) into a mixed number: \[ \frac{15}{8} = 1 \frac{7}{8} \]
Therefore, the amount of apples Michael needs is \( 1 \frac{7}{8} \) pounds.
The answer is \( 1 \frac{7}{8} \) pounds.