Explain Multi-Digit Multiplication with Partial Products
Split the two-digit factor into tens and ones.
About 25 minutes, plus any extended practice
Supplied materials
- Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
- Supplied worked-case record: For 34×26, split twenty-six into twenty and six.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
A multi-digit factor can be decomposed into its place-value parts. Multiply each part by the other factor and add all partial products. A written algorithm organizes the same calculation compactly. The tens-row product represents tens, so its place value must remain visible rather than shifted accidentally.
Split the two-digit factor into tens and ones. Multiply both parts by the other supplied factor, then add the partial products. Check with an estimate and state how the place-value split preserves the original multiplication.
Write the tens partial product with its full value. Every part of the split factor must be multiplied. Draw an area rectangle split into tens-width and ones-width sections.
- Draw an area rectangle split into tens-width and ones-width sections.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Split the two-digit factor into tens and ones.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
For 34×26, split twenty-six into twenty and six. Products are 34×20=680 and 34×6=204. Their sum is 884. A rough check 30×30=900 is nearby. Treating the twenty as two would lose a factor of ten in that partial product. Write the tens partial product with its full value. Every part of the split factor must be multiplied. Draw an area rectangle split into tens-width and ones-width sections.
Check your reasoning
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Helpful tips
- Write the tens partial product with its full value.
- Every part of the split factor must be multiplied.
See the answer and explanation
713
Split a factor into tens and ones and combine both products. The result is 713.
Take it further
Find 47×18. Expected: 470+376=846.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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