Multiplication of multi-digit whole numbers is understood through place value, the distributive property, and the interpretation of each partial product as a product of place-value units, such as tens or hundreds. Accurate computation includes decomposing factors or applying the standard algorithm, aligning partial products, and composing and regrouping quantities while recognizing the role of zero place holders; estimation and area or array representations support reasonableness. The scope is whole-number factors, excluding decimals, fractions, variables, and more abstract generalizations.
To multiply multi-digit whole numbers, break one factor into its place-value parts. Then multiply each part and add the partial products.
Example: Find .
First, decompose into tens and ones:
Use the distributive property:
Multiply by each part:
The second product is multiplied by , not just $2`, so it has a zero in the ones place.
Now add the partial products:
Therefore,
Using the standard algorithm shows the same work:
The first row multiplies by ones. The second row multiplies by tens, so it is shifted one place to the left, or written with a zero placeholder. Finally, add the partial products.
To check that the answer is reasonable, estimate:
so
The exact answer, , is reasonably close to this estimate.
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