Question

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 = 60
c. 3\frac{3}{4}=

Explanation:

Step1: Understand division concept

We have a 15 - foot rope divided into 4 equal parts. Division gives the size of each part. The formula for finding the length of each part when a total length $L$ is divided into $n$ equal parts is $L\div n$. Here $L = 15$ and $n = 4$, so $15\div4$ represents the length of each part.

Step2: Analyze multiplication expression

The expression $4\times15$ means adding 15 four - times or adding 4 fifteen - times. It gives the total length when we have 4 pieces of 15 - foot ropes or 15 pieces of 4 - foot ropes, not the length of each part of a 15 - foot rope divided into 4 parts.

Step3: Convert mixed - number

We convert the mixed number $3\frac{3}{4}$ to an improper fraction. $3\frac{3}{4}=\frac{3\times4 + 3}{4}=\frac{12 + 3}{4}=\frac{15}{4}=15\div4$. So it represents the length of each part.

Answer:

a. Represents the length of each part because dividing the total length 15 feet by the number of parts 4 gives the length of each part.
b. Does not represent the length of each part. It gives the total length when combining 4 pieces of 15 - foot ropes.
c. Represents the length of each part as it is equivalent to $15\div4$.