How many pieces each of length `3(3)/(4)m` can be cut from a rope of length `30 m` ?

Options

A. `5`
B. `6`
C. `8`
D. `2`

Answer

To solve the problem of how many pieces of length \(3 \frac{3}{4} \, m\) can be cut from a rope of length \(30 \, m\), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The length of each piece is given as \(3 \frac{3}{4} \, m\). We need to convert this mixed number into an improper fraction.

\[ 3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \, m \]

### Step 2: Set up the equation to find the number of pieces
We know that the total length of the rope is \(30 \, m\) and the length of each piece is \(\frac{15}{4} \, m\). We can use the formula:

\[ \text{Number of pieces} = \frac{\text{Total Length}}{\text{Length of each piece}} \]

Substituting the values we have:

\[ \text{Number of pieces} = \frac{30}{\frac{15}{4}} \]

### Step 3: Simplify the division
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the equation as:

\[ \text{Number of pieces} = 30 \times \frac{4}{15} \]

### Step 4: Perform the multiplication
Now we can simplify this expression:

\[ \text{Number of pieces} = \frac{30 \times 4}{15} \]

Calculating the numerator:

\[ 30 \times 4 = 120 \]

Now, divide by \(15\):

\[ \text{Number of pieces} = \frac{120}{15} = 8 \]

### Final Answer
Thus, the number of pieces that can be cut from the rope is \(8\).

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