A rope of length `18'1/2` m is cut into equal pieces of `1'7/30` m each. Find the number of pieces.

Explanation

To solve the problem of how many equal pieces of rope can be cut from a length of `18 1/2` meters when each piece is `1 7/30` meters long, we will follow these steps:

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

1. **Convert `18 1/2` to an improper fraction:**
- The whole number part is 18, and the fractional part is `1/2`.
- To convert, multiply the whole number by the denominator and add the numerator:
\[ 18 \times 2 + 1 = 36 + 1 = 37 \]
- So, `18 1/2` can be written as:
\[ \frac{37}{2} \]

2. **Convert `1 7/30` to an improper fraction:**
- The whole number part is 1, and the fractional part is `7/30`.
- To convert, multiply the whole number by the denominator and add the numerator:
\[ 1 \times 30 + 7 = 30 + 7 = 37 \]
- So, `1 7/30` can be written as:
\[ \frac{37}{30} \]

### Step 2: Divide the Length of the Rope by the Length of Each Piece
Now we need to divide the total length of the rope by the length of each piece to find the number of pieces.

\[ \text{Number of pieces} = \frac{\text{Length of rope}}{\text{Length of each piece}} = \frac{\frac{37}{2}}{\frac{37}{30}} \]

### Step 3: Simplify the Division of Fractions
When dividing fractions, we multiply by the reciprocal of the divisor:

\[ \frac{37}{2} \div \frac{37}{30} = \frac{37}{2} \times \frac{30}{37} \]

### Step 4: Cancel Common Factors
We can cancel the `37` in the numerator and denominator:

\[ = \frac{30}{2} = 15 \]

### Conclusion
Thus, the number of pieces the rope can be cut into is **15**.

---