Jacob cut a 126 centimeter rope into 4 equal pieces. How long is each new piece of rope? Check your work! Each piece of rope is \( \square \mathrm{cm} \) long.

To find the length of each piece of rope, we need to divide the total length of the rope by the number of pieces. The total length of the rope is 126 centimeters, and it is cut into 4 equal pieces. We can calculate the length of each piece as follows: \[ \text{Length of each piece} = \frac{\text{Total length}}{\text{Number of pieces}} = \frac{126 \, \text{cm}}{4} \] Now, performing the division: \[ \frac{126}{4} = 31.5 \] So, each piece of rope is \( 31.5 \, \text{cm} \) long. To check our work, we can multiply the length of one piece by the number of pieces: \[ 31.5 \, \text{cm} \times 4 = 126 \, \text{cm} \] Since this matches the original length of the rope, our calculation is correct. Thus, each piece of rope is \( \boxed{31.5} \, \text{cm} \) long.