Stage 14 of 20
The Distributive Trick
Break a hard factor into friendly parts: ×4 as double-double, ×8 as three doubles, ×6 as ×5 + ×1, and so on.
Rewrite the factor
For 7 × 8: double 7 three times (14, 28, 56) or use 7 × 10 − 7 × 2. Distribution means you never face an unfamiliar fact alone — you rebuild it from known pieces.
Why this mental math skill matters
The distributive property turns unfamiliar products into sums of known parts. It is real algebra thinking in kid-friendly clothing.
Worked examples
Study each example slowly. Say the steps aloud — verbal rehearsal strengthens mental arithmetic memory.
6 × 7
- 6 × 5 = 30.
- 6 × 2 = 12.
- 30 + 12 = 42.
Answer: 42
8 × 7
- Double 7 → 14.
- Double 14 → 28.
- Double 28 → 56.
Answer: 56
4 × 9
- Double 9 → 18.
- Double 18 → 36.
Answer: 36
Tips for success
- Pick the rewrite that uses facts you already trust.
- Keep partial products organized.
- Say the property in words: “six sevens is five sevens plus one seven.”
Common mistakes to avoid
- Rewriting both factors at once and losing track.
- Adding partial products incorrectly at the end.
How to practice this stage
Rewrite one factor every time (×6 as ×5+×1, ×8 as double-double-double). Check with a second method once per session.
Interactive practice
Stage 14 Drill
Break factors into easier parts, then combine.
Solve
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FAQ: The Distributive Trick
How does the distributive trick help mental math?
It lets you break a hard multiplication into easier multiplications you already know, then combine.
Is double-double the same as ×4?
Yes — doubling twice multiplies by 4; doubling three times multiplies by 8.