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Use the standard multiplication algorithm

Multiplication of multi-digit whole numbers is understood as combining place-value-scaled partial products: each digit of one factor multiplies the other factor, and its place determines the corresponding shift in the written product. The standard algorithm records these products compactly, uses regrouping when products exceed nine, and combines them accurately; estimation and place-value reasoning help detect misplaced digits or omitted regrouping. This treatment excludes decimal, fraction, and algebraic extensions.

Detailed Explanation: Use the standard multiplication algorithm

Each digit in one factor creates a partial product. Its place value tells you where that product belongs. Start with the ones digit, then move left.

Example:

246×37246 \times 37

First, multiply by the ones digit, 77:

  1. 7×6=427 \times 6=42. Write 22 in the ones place and carry 44.
  2. 7×4+4=327 \times 4+4=32. Write 22 in the tens place and carry 33.
  3. 7×2+3=177 \times 2+3=17. Write 1717 in the hundreds and thousands places.

So,

246×7=1722246 \times 7=1722

Next, multiply by the tens digit, 33. Since 33 represents 3030, the answer belongs one place to the left:

  1. 3×6=183 \times 6=18. Write 88 and carry 11.
  2. 3×4+1=133 \times 4+1=13. Write 33 and carry 11.
  3. 3×2+1=73 \times 2+1=7.

This gives 738738, shifted one place left, or 73807380.

Write and add the partial products:

0246×037172273809102\begin{array}{r} \phantom{0}246\\ \times\phantom{0}37\\ \hline 1722\\ 7380\\ \hline 9102 \end{array}

Therefore,

246×37=9102\boxed{246 \times 37=9102}

Check your answer with an estimate:

250×40=10,000250 \times 40=10{,}000

Since 9,1029{,}102 is close to 10,00010{,}000, the answer is reasonable.

Learn by doing: Use the standard multiplication algorithm

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