Multiply a 3-digit number by a 2-digit number

Multiplying a whole number from 100–999 by one from 10–99 involves decomposing the factors by place value and combining partial products through the distributive property, with regrouping when needed. Area models, equations, and the standard algorithm show why the tens partial product is shifted one place and support estimation to check reasonableness; this scope excludes decimal factors, larger or more general multidigit cases, and symbolic extensions.

Detailed Explanation: Multiply a 3-digit number by a 2-digit number

To multiply a 3-digit number by a 2-digit number, break the 2-digit number into tens and ones. Then multiply the 3-digit number by each part and add the partial products.

Example: Find $347 \times 26$ .

1. Decompose the 2-digit number

The number $26$ has $2$ tens and $6$ ones:

26=20+6

So,

347 \times 26=347 \times (20+6)

2. Find the partial products

Multiply by the ones:

347 \times 6=2{,}082

Multiply by the tens:

347 \times 20=6{,}940

The zero appears because $20$ is $2$ tens, not $2$ ones.

3. Add the partial products

\begin{array}{r} 2{,}082\\ + 6{,}940\\ \hline 9{,}022 \end{array}

Therefore,

\boxed{347 \times 26=9{,}022}

Using the standard algorithm, the work looks like this:

\begin{array}{r} \ \ 347\\ \times\ \ 26\\ \hline 2{,}082 \quad \text{(347 times 6)}\\ + 6{,}940 \quad \text{(347 times 20)}\\ \hline 9{,}022 \end{array}

The second row is shifted one place to the left because it represents tens.

You can estimate to check your answer:

347 \times 26 \approx 350 \times 30=10{,}500

Since $9{,}022$ is reasonably close to $10{,}500$ , the answer makes sense.

Learn by doing: Multiply a 3-digit number by a 2-digit number

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Multiplication - Whole Number 3 x 2 - Columns

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