How many pieces of length 3 `5/7` m each can be cut from a wall paper 52 m long

Answer

To solve the problem of how many pieces of length \(3 \frac{5}{7}\) m each can be cut from a wallpaper that is 52 m long, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The length of each piece is given as \(3 \frac{5}{7}\). To convert this to an improper fraction:
\[ 3 \frac{5}{7} = \frac{(3 \times 7) + 5}{7} = \frac{21 + 5}{7} = \frac{26}{7} \]

### Step 2: Set up the equation for the number of pieces
Let \(x\) be the number of pieces that can be cut from the wallpaper. The total length of the pieces cut must equal the total length of the wallpaper:
\[ \text{Length of each piece} \times \text{Number of pieces} = \text{Total length of wallpaper} \]
This can be expressed as:
\[ \frac{26}{7} \times x = 52 \]

### Step 3: Solve for \(x\)
To find \(x\), we can rearrange the equation:
\[ x = \frac{52}{\frac{26}{7}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ x = 52 \times \frac{7}{26} \]

### Step 4: Simplify the expression
Now, we simplify:
\[ x = \frac{52 \times 7}{26} \]
We can simplify \(52\) and \(26\):
\[ 52 = 2 \times 26 \quad \Rightarrow \quad \frac{52}{26} = 2 \]
Thus, we have:
\[ x = 2 \times 7 = 14 \]

### Conclusion
Therefore, the number of pieces that can be cut from the wallpaper is \(14\).

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