Skill: Multiply a 2-digit number by a 1-digit number using partial products

Explanation and Free Practice Resources

The learner understands that a two-digit factor can be decomposed into tens and ones, then each part can be multiplied by the one-digit factor and the resulting partial products added: $23 \times 4=(20\times4)+(3\times4)=80+12=92$ . An area model or place-value equations can show why the partial products represent distinct place-value contributions and why they must be combined, supporting later work with the distributive property and multi-digit multiplication; this scope does not include multiplying two multi-digit factors or more advanced algorithmic generalizations.

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Detailed Explanation: Multiply a 2-digit number by a 1-digit number using partial products

To multiply a 2-digit number by a 1-digit number, split the 2-digit number into tens and ones. Multiply each part, then add the partial products.

Example: Find $23 \times 4$ .

Break $23$ into tens and ones:

23=20+3

Multiply each part by $4$ :

20\times4=80

3\times4=12

Add the two partial products:

80+12=92

Therefore,

23\times4=(20\times4)+(3\times4)=80+12=\boxed{92}

The $80$ shows the value from the tens, and the $12$ shows the value from the ones. Combining them gives the total, $92$ .

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Multiplication Area Model - Twenties to Total

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