Bot GPT 4-o mini To determine how many pieces of length \( \frac{1}{56} \) meters can be cut from a rod that is \( \frac{7}{8} \) meters long, we need to divide the total length of the rod by the length of each piece.
First, we perform the division:
\[ \text{Number of pieces} = \frac{\text{Length of rod}}{\text{Length of each piece}} = \frac{\frac{7}{8}}{\frac{1}{56}} \]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ \frac{7}{8} \div \frac{1}{56} = \frac{7}{8} \times 56 \]
Next, we simplify \( \frac{7}{8} \times 56 \):
\[ \frac{7 \times 56}{8} = \frac{392}{8} \]
Now we divide \( 392 \) by \( 8 \):
\[ 392 \div 8 = 49 \]
Thus, the total number of pieces that can be cut from the rod is
\[ \boxed{49} \]
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