A ribbon of length `5(1/4)` m is cut into small pieces each of length `3/4`
Number of pieces will be:

Options

A. 5
B. 6
C. 7
D. 8

Answer

To find the number of pieces a ribbon of length \(5 \frac{1}{4}\) meters can be cut into, where each piece is \( \frac{3}{4} \) meters long, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The length of the ribbon is given as \(5 \frac{1}{4}\) meters. We need to convert this mixed number into an improper fraction.

\[ 5 \frac{1}{4} = \frac{(5 \times 4) + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} \text{ meters} \]

### Step 2: Set up the equation for the number of pieces
Let \(X\) be the number of pieces. Each piece is \( \frac{3}{4} \) meters long. Therefore, the total length of \(X\) pieces is:

\[ \text{Length of } X \text{ pieces} = X \times \frac{3}{4} \]

### Step 3: Equate the total length of the pieces to the length of the ribbon
The total length of the pieces must equal the length of the ribbon:

\[ X \times \frac{3}{4} = \frac{21}{4} \]

### Step 4: Solve for \(X\)
To solve for \(X\), we can multiply both sides of the equation by \(4\) to eliminate the fraction:

\[ 4 \times (X \times \frac{3}{4}) = 4 \times \frac{21}{4} \]

This simplifies to:

\[ 3X = 21 \]

Now, divide both sides by \(3\):

\[ X = \frac{21}{3} = 7 \]

### Conclusion
The number of pieces the ribbon can be cut into is \(7\).

---