35. A piece of coaxial cable \( \frac{4}{5} \) meter long is to be cut into 8 pieces of the same length. What is the length of each piece?

We are given the length of the cable as \( \frac{4}{5} \) meter and need to cut it into 8 equal pieces. 1. Set up the division of the total length by the number of pieces: \[ \text{Length of each piece} = \frac{4}{5} \div 8 \] 2. Convert the division to multiplication by the reciprocal: \[ \text{Length of each piece} = \frac{4}{5} \times \frac{1}{8} \] 3. Multiply the fractions: \[ \text{Length of each piece} = \frac{4 \times 1}{5 \times 8} = \frac{4}{40} \] 4. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 4: \[ \frac{4 \div 4}{40 \div 4} = \frac{1}{10} \] Thus, each piece is \( \frac{1}{10} \) meter long.