Multi-Digit Multiplication Practice Problems & Standard Algorithm Worked Solutions
Master multi-digit multiplication using the standard algorithm, partial products (box method), and expanded place-value decomposition. Practice 2-digit by 1-digit, 3-digit by 1-digit, and 2-digit by 2-digit calculations with step-by-step carrying explanations.
🧠 Core Problem-Solving Strategies
📦 Area / Box Method (Partial Products)
Break numbers by place value: 34 × 6 = (30 × 6) + (4 × 6) = 180 + 24 = 204.
🏗️ Standard Column Algorithm
Multiply ones digit first, regroup carrying digits into the tens column, then add intermediate lines.
⚡ Double and Halve Shortcut
For even factors: 18 × 15 = 9 × 30 = 270 (halve 18 to 9, double 15 to 30).
❓ Frequently Asked Questions
How do you multiply two 2-digit numbers step-by-step?
First, multiply the top number by the ones digit of the bottom number. Next, place a placeholder 0 and multiply by the tens digit. Finally, sum both partial product rows.
Why must we put a zero in the second row of 2-digit multiplication?
Because you are multiplying by the tens digit (e.g., 20 instead of 2). The placeholder zero shifts the partial product to its correct tens place value.
Continue Learning & Practicing
Reinforce your understanding with printable worksheets, step-by-step guides, calculators, and speed games: