Multiply a 2-digit number by a 1-digit number using models

A two-digit quantity multiplied by a one-digit quantity can be decomposed by place value: for example, $23 \times 4=(20\times4)+(3\times4)$ . Arrays, area models, and base-ten representations show the equal groups, partial products, and regrouping of ten ones into a ten, supporting accurate interpretation of the product rather than treating digits independently. This scope does not include multiplying two two-digit numbers or applying a fully generalized multi-digit algorithm.

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

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

Example: $23 \times 4$

Think of this as 4 equal groups of 23:

23+23+23+23

Break $23$ into $20+3$ :

23 \times 4=(20+3)\times 4

Use an area model:

\begin{array}{c|c} 20 & 3\\ \hline 20\times4 & 3\times4 \end{array}

Now multiply each part:

$20\times4=80$
$3\times4=12$

Add the partial products:

80+12=92

So,

\boxed{23\times4=92}

The $12$ ones can also be regrouped as $1$ ten and $2$ ones. Then $8$ tens plus $1$ ten is $9$ tens, with $2$ ones left. That makes $92$ .

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Multiplication Area Model - Twenties to Total

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