How many pieces each `5""1/6` metres long can be cut from a cloth `77""1/2` metres long?

Answer

To solve the problem of how many pieces each `5 1/6` meters long can be cut from a cloth `77 1/2` meters long, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

- For `5 1/6`:
\[ 5 \frac{1}{6} = \frac{5 \times 6 + 1}{6} = \frac{30 + 1}{6} = \frac{31}{6} \]

- For `77 1/2`:
\[ 77 \frac{1}{2} = \frac{77 \times 2 + 1}{2} = \frac{154 + 1}{2} = \frac{155}{2} \]

### Step 2: Set Up the Equation
Let \( x \) be the number of pieces that can be cut from the cloth. The total length of the cloth can be expressed as:
\[ x \times \frac{31}{6} = \frac{155}{2} \]

### Step 3: Solve for \( x \)
To find \( x \), we need to isolate it. We can do this by multiplying both sides by the reciprocal of \( \frac{31}{6} \):
\[ x = \frac{155}{2} \div \frac{31}{6} = \frac{155}{2} \times \frac{6}{31} \]

### Step 4: Simplify the Expression
Now, we can simplify the expression:
\[ x = \frac{155 \times 6}{2 \times 31} \]
Calculating the numerator and denominator:
- \( 155 \div 31 = 5 \)
- \( 6 \div 2 = 3 \)

So,
\[ x = 5 \times 3 = 15 \]

### Final Answer
Thus, the number of pieces that can be cut from the cloth is \( \boxed{15} \).

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