Protein synthesis worksheet how to - Free Printable

Problem Analysis:

The task involves completing a sequence of operations using the Pascaline, an early mechanical calculator invented by Blaise Pascal. The goal is to perform arithmetic operations (addition and subtraction) step by step, following the rules provided in the instructions.

#### Key Instructions:
1. Addition: To add numbers, turn the wheels clockwise.
2. Subtraction: To subtract numbers, turn the wheels counterclockwise.
3. Carry/Borrow: If a carry or borrow occurs during addition or subtraction, it must be handled appropriately.
4. Final Answer: The result should be read from the display after all operations are completed.

#### Provided Data:
- Initial value: `0000`
- Operations to perform:
- Add `1234`
- Subtract `567`
- Add `89`

Step-by-Step Solution:

#### Step 1: Start with the initial value
The initial value on the Pascaline is `0000`.

#### Step 2: Add `1234`
To add `1234`, we turn the wheels clockwise for each digit:
- Turn the rightmost wheel (`units place`) clockwise by 4.
- Turn the next wheel (`tens place`) clockwise by 3.
- Turn the next wheel (`hundreds place`) clockwise by 2.
- Turn the leftmost wheel (`thousands place`) clockwise by 1.

After adding `1234`, the display shows:
```
0000 + 1234 = 1234
```

#### Step 3: Subtract `567`
To subtract `567`, we turn the wheels counterclockwise for each digit:
- Turn the rightmost wheel (`units place`) counterclockwise by 7.
- Turn the next wheel (`tens place`) counterclockwise by 6.
- Turn the next wheel (`hundreds place`) counterclockwise by 5.

During this operation, borrowing may occur if a digit being subtracted is larger than the current digit on the wheel. Let's calculate step by step:

1. Units place: Subtract 7 from 4.
- Since 4 < 7, we need to borrow 1 from the tens place. This makes the units place `14` (after borrowing).
- Subtract 7 from 14: \(14 - 7 = 7\).
- The units place now shows `7`.

2. Tens place: After borrowing, the tens place is now `2 - 1 = 1`. Subtract 6 from 1.
- Since 1 < 6, we need to borrow 1 from the hundreds place. This makes the tens place `11` (after borrowing).
- Subtract 6 from 11: \(11 - 6 = 5\).
- The tens place now shows `5`.

3. Hundreds place: After borrowing, the hundreds place is now `2 - 1 = 1`. Subtract 5 from 1.
- Since 1 < 5, we need to borrow 1 from the thousands place. This makes the hundreds place `11` (after borrowing).
- Subtract 5 from 11: \(11 - 5 = 6\).
- The hundreds place now shows `6`.

4. Thousands place: After borrowing, the thousands place is now `1 - 1 = 0`. Subtract 0 from 0:
- The thousands place remains `0`.

After subtracting `567`, the display shows:
```
1234 - 567 = 0667
```

#### Step 4: Add `89`
To add `89`, we turn the wheels clockwise for each digit:
- Turn the rightmost wheel (`units place`) clockwise by 9.
- Turn the next wheel (`tens place`) clockwise by 8.

Let's calculate step by step:

1. Units place: Add 9 to 7.
- \(7 + 9 = 16\). Write down `6` and carry over `1` to the tens place.
- The units place now shows `6`.

2. Tens place: Add 8 to 6, plus the carry-over `1`.
- \(6 + 8 + 1 = 15\). Write down `5` and carry over `1` to the hundreds place.
- The tens place now shows `5`.

3. Hundreds place: Add the carry-over `1` to 6.
- \(6 + 1 = 7\).
- The hundreds place now shows `7`.

4. Thousands place: No change since there is no carry-over to the thousands place.
- The thousands place remains `0`.

After adding `89`, the display shows:
```
0667 + 0089 = 0756
```

Final Answer:

The final result displayed on the Pascaline is:
\[
\boxed{0756}
\]