Advanced Tables Mastery: Tables 6, 7, 8, 9 and the Distributive Property
Step into advanced arithmetic mastery! In this lesson, we unlock the higher multiplication tables: 6, 7, 8, and 9. We learn to wield the powerful 'Distributive Property of Multiplication over Addition' to decompose challenging factors into friendly, familiar numbers (such as breaking 7 into 5 + 2 or 8 into 5 + 3), solving problems like 6 × 8 and 7 × 9 with speed and confidence.
🧮 The Distributive Property
The Distributive Property lets us break a large factor into two smaller addends, multiply each part separately, and add the partial products:
Example: Solving 6 × 7
1. Decompose 7 into (5 + 2).
2. Distribute: 6 × (5 + 2) = (6 × 5) + (6 × 2).
3. Add partial products: 30 + 12 = 42!
Therefore: 6 × 7 = 42.
✨ The Nine's Digit Sum Wonder
In the 9s multiplication table, notice that the digits of the product (up to 9 × 10) always add up to 9:
- 9 × 2 = 18 (1 + 8 = 9)
- 9 × 3 = 27 (2 + 7 = 9)
- 9 × 4 = 36 (3 + 6 = 9)
- 9 × 5 = 45 (4 + 5 = 9)
- 9 × 6 = 54 (5 + 4 = 9)
- 9 × 7 = 63 (6 + 3 = 9)
- 9 × 8 = 72 (7 + 2 = 9)
- 9 × 9 = 81 (8 + 1 = 9)
Distributive Property Applications
Write 7 as (5 + 2).
8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56.
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