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

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: 23×4=(20×4)+(3×4)=80+12=9223 \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.

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 23×423 \times 4.

  1. Break 2323 into tens and ones:

23=20+323=20+3

  1. Multiply each part by 44:

20×4=8020\times4=80 3×4=123\times4=12

  1. Add the two partial products:

80+12=9280+12=92

Therefore,

23×4=(20×4)+(3×4)=80+12=9223\times4=(20\times4)+(3\times4)=80+12=\boxed{92}

The 8080 shows the value from the tens, and the 1212 shows the value from the ones. Combining them gives the total, 9292.

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

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    Multiplication Area Model - Twenties to Total

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