Formal Division of 3 Digit Numbers by 2 Digit Numbers Worksheet - Free Printable

The image shows a worksheet titled "Formal Division of 3 Digit Numbers by 2 Digit Numbers." The task involves solving division problems using the formal method of division. Below, I will explain how to solve one of these problems step-by-step as an example, and then provide the general approach for solving such problems.

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Example Problem:

Let's solve 132 ÷ 12 (Problem 1 from the worksheet).

#### Step 1: Set up the division
Write the problem in the long division format:
```
____
12 | 132
```

#### Step 2: Divide the first digit(s) of the dividend
- The dividend is 132, and the divisor is 12.
- Look at the first digit of the dividend, which is 1. Since 1 is less than 12, consider the first two digits: 13.
- Ask: How many times does 12 go into 13? The answer is 1.

#### Step 3: Multiply and subtract
- Multiply 12 by 1: \( 12 \times 1 = 12 \).
- Subtract this product from 13: \( 13 - 12 = 1 \).

#### Step 4: Bring down the next digit
- Bring down the next digit of the dividend, which is 2. Now you have 12.

#### Step 5: Repeat the division process
- Ask: How many times does 12 go into 12? The answer is 1.
- Multiply 12 by 1: \( 12 \times 1 = 12 \).
- Subtract this product from 12: \( 12 - 12 = 0 \).

#### Step 6: Write the quotient
- The quotient is 11, and the remainder is 0.

So, 132 ÷ 12 = 11.

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General Approach for Solving These Problems:

1. Set up the division: Write the dividend inside the division bracket and the divisor outside.
2. Divide: Starting from the leftmost digit(s) of the dividend, determine how many times the divisor can fit into that part of the dividend.
3. Multiply: Multiply the divisor by the quotient obtained in the previous step.
4. Subtract: Subtract the product from the part of the dividend you considered.
5. Bring down: Bring down the next digit of the dividend and repeat the process until all digits are used.
6. Write the final answer: The result is the quotient, and if there is any remainder, it is written separately.

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Solving Another Problem:

Let's solve 378 ÷ 18 (Problem 16 from the worksheet).

#### Step 1: Set up the division
```
____
18 | 378
```

#### Step 2: Divide the first digit(s) of the dividend
- Consider the first two digits of the dividend, which is 37.
- Ask: How many times does 18 go into 37? The answer is 2.
- Multiply 18 by 2: \( 18 \times 2 = 36 \).
- Subtract: \( 37 - 36 = 1 \).

#### Step 3: Bring down the next digit
- Bring down the next digit, which is 8. Now you have 18.

#### Step 4: Repeat the division process
- Ask: How many times does 18 go into 18? The answer is 1.
- Multiply 18 by 1: \( 18 \times 1 = 18 \).
- Subtract: \( 18 - 18 = 0 \).

#### Step 5: Write the quotient
- The quotient is 21, and the remainder is 0.

So, 378 ÷ 18 = 21.

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Final Answer:

The solutions to the problems can be filled in the worksheet accordingly. For the example problems:
- 1. 132 ÷ 12 = 11
- 16. 378 ÷ 18 = 21

If you need solutions for other specific problems, let me know!

Final Answer: \boxed{11 \text{ and } 21} for the examples provided.