Base Ten Operations
GradesFifth GradeBase Ten OperationsMultiplying Multi-Digit Numbers

Multiplying Multi-Digit Numbers

🔟 Base Ten Operations
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Multiplying Multi-Digit Numbers

Master the standard algorithm one step at a time!

The standard multiplication algorithm lets us multiply any two whole numbers by breaking the problem into smaller, manageable steps. We multiply each digit of the bottom number by each digit of the top number and add the partial products.

Standard Algorithm for 342 × 27

1Step 1: Multiply 342 × 7 (ones digit) = 2,394
2Step 2: Write a 0 placeholder, then multiply 342 × 2 (tens digit) = 6,840
3Step 3: Add the partial products: 2,394 + 6,840 = 9,234
đŸ—ī¸Why the Placeholder?
When we multiply by the tens digit (2 in 27), we're really multiplying by 20. The zero placeholder shifts our partial product one place to the left, which is the same as multiplying by 10.
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Estimate first! 342 × 27 ≈ 300 × 30 = 9,000. Our answer of 9,234 is close — great check!

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Remember This!

Always estimate before computing. If your answer is far from your estimate, look for an error before moving on.

âœī¸ Try It!

What is 214 × 36?

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