A ribbon of lengh `110.5` m is cut into equal ribbon pieces of length `8.5 cm.` Find the number of ribbon piees thus obtained.

Answer

To find the number of ribbon pieces obtained from a ribbon of length 110.5 meters cut into pieces of length 8.5 centimeters, we can follow these steps:

### Step 1: Convert the lengths to the same unit
We have the total length of the ribbon in meters (110.5 m) and the length of each piece in centimeters (8.5 cm). To make calculations easier, we will convert the length of each piece from centimeters to meters.

\[ 8.5 \text{ cm} = \frac{8.5}{100} \text{ m} = 0.085 \text{ m} \]

### Step 2: Set up the equation
Let \( x \) be the number of ribbon pieces. The total length of the ribbon can be expressed as:

\[ 110.5 \text{ m} = x \times 0.085 \text{ m} \]

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

\[ x = \frac{110.5 \text{ m}}{0.085 \text{ m}} \]

### Step 4: Remove decimals for easier calculation
To simplify the division, we can eliminate the decimals by multiplying both the numerator and the denominator by 1000 (to shift the decimal point three places to the right):

\[ x = \frac{110.5 \times 1000}{0.085 \times 1000} = \frac{110500}{85} \]

### Step 5: Perform the division
Now, we will divide 110500 by 85:

1. **Calculate how many times 85 goes into 110500**:
- 85 goes into 110 (1 time), leaving a remainder of 25.
- Bring down the next digit (0) to make it 250.
- 85 goes into 250 (2 times), leaving a remainder of 80.
- Bring down the next digit (0) to make it 800.
- 85 goes into 800 (9 times), leaving a remainder of 35.
- Bring down the next digit (0) to make it 350.
- 85 goes into 350 (4 times), leaving a remainder of 10.
- Bring down the next digit (0) to make it 100.
- 85 goes into 100 (1 time), leaving a remainder of 15.
- Bring down the next digit (0) to make it 150.
- 85 goes into 150 (1 time), leaving a remainder of 65.
- Bring down the next digit (0) to make it 650.
- 85 goes into 650 (7 times), leaving a remainder of 55.
- Bring down the next digit (0) to make it 550.
- 85 goes into 550 (6 times), leaving a remainder of 40.
- Bring down the next digit (0) to make it 400.
- 85 goes into 400 (4 times), leaving a remainder of 60.
- Bring down the next digit (0) to make it 600.
- 85 goes into 600 (7 times), leaving a remainder of 5.
- Bring down the next digit (0) to make it 50.
- 85 goes into 50 (0 times).

After performing the division, we find:

\[ x = 1300 \]

### Final Answer
The number of ribbon pieces obtained is **1300**.

---