Multi-digit problems involve using multiplication and division with numbers that have more than one digit. These problems may require multiple steps, and understanding the processes of long multiplication and long division is essential. The goal is to break down the problem into smaller, more manageable parts.

In multi-digit multiplication and division, you may need to work with two or more digits in both the numbers you're multiplying or dividing. This requires using place value and carrying over or borrowing numbers.

Examples:

Example 1: Multi-digit Multiplication
Multiply 46 by 12:
Step 1: Multiply the ones place: 6 × 2 = 12. Write down 2 and carry over 1.
Step 2: Multiply the tens place: 4 × 2 = 8, then add the carry-over (1): 8 + 1 = 9.
Step 3: Multiply the ones place of 46 by 1 (which is in the tens place of 12): 6 × 1 = 6.
Step 4: Multiply the tens place of 46 by 1: 4 × 1 = 4.
Step 5: Add the results together: 92 + 460 = 552.
Final result: 46 × 12 = 552.

Example 2: Multi-digit Division
Divide 785 by 23:
Step 1: Divide the first part (78) by 23. 23 goes into 78 three times, so write down 3.
Step 2: Multiply 3 by 23, which equals 69. Subtract 69 from 78, leaving a remainder of 9.
Step 3: Bring down the next digit (5), making the number 95.
Step 4: Divide 95 by 23. 23 goes into 95 four times, so write down 4.
Final result: 785 ÷ 23 = 34 with a remainder of 3.

Multi-digit problems may seem more complicated, but with practice, they become much easier to solve. These problems are important because they show how we use basic operations with larger numbers in the real world.

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