Skill: Apply the distributive property

Explanation and Free Practice Resources

The distributive property explains that multiplying a whole number by a sum or difference gives the same result as multiplying each part and then combining the partial products, as in $6(20+3)=6\cdot20+6\cdot3$ . Decomposing factors by place value supports efficient computation and reveals the connection between arrays, area, and multiplication; the scope is limited to numerical whole-number expressions, not negative or rational numbers or symbolic polynomial expansion.

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Detailed Explanation: Apply the distributive property

To use the distributive property, break apart a number into friendly parts, multiply each part, and then add the partial products.

For example, find:

6 \times 23

Break $23$ into tens and ones:

23=20+3

Rewrite the multiplication:

6 \times 23=6(20+3)

Multiply $6$ by each part:

6(20+3)=6 \times 20+6 \times 3

Find the partial products:

6 \times 20=120 \qquad \text{and} \qquad 6 \times 3=18

Combine them:

120+18=138

Therefore,

\boxed{6 \times 23=138}

The distributive property lets you multiply by each place-value part and combine the results.

Learn by doing: Apply the distributive property

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Multiplication Area Model - Twenties to Total from Sum

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