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}

Explanation:

Step1: Understand division concept

When we divide a total length by the number of parts, we get the length of each part. The total length of the rope is 15 feet and we want to divide it into 4 equal - parts. The operation for this is division, so 15÷4 represents the length of each part.

Step2: Analyze multiplication expression

The expression 4×15 means we are multiplying the number of parts (4) by the total length (15), which is not what we want. We want to split the 15 - foot rope into 4 parts, not find the product of 4 and 15.

Step3: Convert improper fraction

We know that 15÷4 = $\frac{15}{4}$. Converting $\frac{15}{4}$ to a mixed - number, we divide 15 by 4. 4 goes into 15 three times with a remainder of 3. So, $\frac{15}{4}=3\frac{3}{4}$.

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 as it is a multiplication operation and not relevant to splitting the rope into parts.
c. Represents the length of each part as $3\frac{3}{4}=\frac{15}{4}$ which is the result of 15÷4.