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Leaving out a partial product

Every part of one factor multiplies every part of the other. A rectangle split into regions helps keep track.

Spot the wrong turn

Find 24 × 3 with partial products.

Incorrect answer: 18

For two two-part factors, there are four partial products. Multiplying only tens by tens and ones by ones misses the two cross-products.

Work it through

The correction

72

20 × 3 + 4 × 3 = 60 + 12.

  1. Break each factor into tens and ones.
  2. Multiply every part of the first factor by every part of the second.
  3. Add all partial products and compare with an estimate.

Try the reasoning in another example

Find 32 × 15.

  1. Use (30 + 2)(10 + 5).
  2. Partial products are 300, 150, 20, and 10.
  3. Add 300 + 150 + 20 + 10.

Answer: 480

Explain why each step preserves the quantity or relationship. If you can compute the answer but cannot explain the step, revisit the model before adding more questions.

The short check below reuses the first example as a retrieval question and adds a second question. It checks this method; it does not establish a grade level.

Your next step

Check this step for yourself

2 questions · No time limit

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1 Find 24 × 3 with partial products.
2 Find 21 × 12.