Question

section b: practice problems

1. han cuts a 15 - foot piece of rope into 4 equal parts. decide whether each expression represents the length of each part of the rope in feet. explain or show your reasoning.

a. 15÷4
b. 4×15
c. 3\frac{3}{4}
(from unit 2, lesson 6.)

Explanation:

Step1: Recall division concept

When dividing a total length into equal - sized parts, we use division. The total length of the rope is 15 feet and we want to divide it into 4 equal parts. The formula for finding the length of each part is $\text{Length of each part}=\frac{\text{Total length}}{\text{Number of parts}}$. So, $15\div4$ represents the length of each part.

Step2: Analyze multiplication

$4\times15$ represents 4 groups of 15. It does not represent dividing 15 into 4 equal parts.

Step3: Convert division to mixed - number

$15\div4=\frac{15}{4}=3\frac{3}{4}$. So, $3\frac{3}{4}$ also represents the length of each part.

Answer:

a. Represents the length of each part. Reason: Division of total length by number of parts.
b. Does not represent the length of each part. Reason: It is a multiplication, not a division for equal - part splitting.
c. Represents the length of each part. Reason: Equivalent to $15\div4$.