Distributive Property of Multiplication

See the property, then use it to break hard multiplication facts.

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TRY THESE PROBLEMS

💡 Change a, b, or c to see both ways to solve the same total.

💡 Stuck on a hard fact? Tap Split at 5 to break one factor into 5 + the rest.

💡 You multiplied the easier pieces and added. Tap Reset to try another fact.

Enter valid numbers (a: 1–10; b and c: 0–10) so b + c is at most 10.

7 × ( 5 + 3 )

This equation can be solved in 2 ways:

7 × 5 + 7 × 3

7 × 5 = 35

7 times 5

7 × 3 = 21

7 times 3

35 + 21

56

7 × 8

7 × 8 = 56

7 times 8

56

Try a harder fact like 7 × 8. Facts where both factors are 5 or less don't need this break-apart strategy.

8 = 5 + 3

So, ( 5 + 3 ) × 8

So, 7 × ( 5 + 3 )

which is equal to

5 × 8 + 3 × 8

7 × 5 + 7 × 3

5 × 8 = 40

5 times 8

3 × 8 = 24

3 times 8

40 + 24

64

📖 Teacher note: Start in Theoretical mode so students see that a × (b + c) and (a × b) + (a × c) are two ways to solve the same problem. Then switch to Strategic for hard facts like 7 × 8: split one factor at 5, multiply the easier pieces, and add. This mirrors how many Grade 3 lessons introduce the distributive property before mental-math strategies.

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More teacher tools: Back to all teacher tools · Multiplication Array Maker · Times Table Explorer · Doubles & Near Doubles · Number Bonds