Multi-Digit Multiplication Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multi-Digit Multiplication.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Multiplying numbers with two or more digits using the standard algorithm, partial products, or the area (box) model.
Think of a rectangle with sides 23 and 47. You can break it into smaller rectangles: 20 \times 40, 20 \times 7, 3 \times 40, and 3 \times 7, then add the pieces. That's partial products—the standard algorithm just organizes this neatly.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Multi-digit multiplication uses the distributive property to break a hard problem into easier single-digit multiplications.
Common stuck point: Remembering to shift partial products left (multiply by 10, 100, etc.) when multiplying by tens and hundreds digits.
Sense of Study hint: Break one factor into place-value parts (e.g., 23 = 20 + 3), multiply each part separately, then add the results.
Worked Examples
Example 1
easySolution
- 1 Multiply 47 by 6 (ones digit of 36): 47 \times 6 = 282.
- 2 Multiply 47 by 30 (tens digit of 36): 47 \times 30 = 1410.
- 3 Add the partial products: 282 + 1410 = 1692.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
mediumExample 2
hardRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.