How many pieces of length `3(3)/(4)` m. can be cut from a rope of length 45 m ?

Answer

To solve the problem of how many pieces of length \(3 \frac{3}{4}\) m can be cut from a rope of length 45 m, we will follow these steps:

### Step 1: Convert the mixed number 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.

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

### Step 2: Set up the equation to find the number of pieces.
Let the number of pieces be \(n\). The total length of the rope is equal to the number of pieces multiplied by the length of each piece.

\[ n \times \frac{15}{4} = 45 \]

### Step 3: Solve for \(n\).
To find \(n\), we can rearrange the equation:

\[ n = \frac{45}{\frac{15}{4}} \]

When dividing by a fraction, we multiply by its reciprocal:

\[ n = 45 \times \frac{4}{15} \]

### Step 4: Simplify the expression.
Now we can simplify \(45 \times \frac{4}{15}\):

\[ n = \frac{45 \times 4}{15} \]

Calculating \(45 \div 15\):

\[ 45 \div 15 = 3 \]

So, we have:

\[ n = 3 \times 4 = 12 \]

### Step 5: Conclusion.
Thus, the number of pieces of length \(3 \frac{3}{4}\) m that can be cut from a rope of length 45 m is:

\[ \boxed{12} \]