Use partial products to multiply

Partial products represent multi-digit whole-number multiplication by decomposing a factor according to place value and applying the distributive property, such as $347 \times 26 = (347 \times 20) + (347 \times 6)$ . The learner connects each partial product to an area-model region or place-value component, aligns and combines products correctly, and understands that the method preserves value rather than treating digits as independent; decimal, fraction, and more abstract algebraic extensions are outside this scope.

Detailed Explanation: Use partial products to multiply

To multiply using partial products, break one factor into its place-value parts, multiply each part, and then add the products.

Example: Find $(347 \times 26)$ .

1. Decompose $(26)$

The $2$ is in the tens place, so it means $(20)$ :

26=20+6

2. Multiply by each part

347\times 20=6{,}940

347\times 6=2{,}082

These are the partial products. Each one shows the product from one place-value part of $(26)$ .

3. Add the partial products

Align the numbers by place value:

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

Therefore,

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

This works because of the distributive property:

347\times 26 =347\times(20+6) =(347\times20)+(347\times6).

The digits in $(26)$ are not treated separately as just $2$ and $6$ ; the $2$ represents $(20)$ because it is in the tens place.

Learn by doing: Use partial products to multiply

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Multiplication - Whole Number 5 x 2

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