Mental Math & The Distributive Property

Multiply Smarter: Using the Distributive Property

Discover the secret to solving big multiplication problems in your head! Learn how to break apart tricky numbers and put them back together for faster mental math.

Part 1: The "Friendly Numbers" Strategy (Addition)

Instructions: Use the distributive property to break one of the factors into a sum of two friendly numbers to solve the problem.
Example: 4 × 52 = 4(50 + 2) = 200 + 8 = 208

1. 6 × 104
2. 8 × 23
3. 14 × 102
4. 5 × 312

Part 2: The "Almost There" Strategy (Subtraction)

Instructions: Use the distributive property to break one of the factors into a difference by rounding up to the nearest friendly number and subtracting.
Example: 7 × 99 = 7(100 - 1) = 700 - 7 = 693

5. 4 × 98
6. 9 × 39
7. 12 × 99
8. 6 × 195

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Answer Key / Step-by-Step Breakdown

Part 1
1. 6 × 104 → 6(100 + 4) = 600 + 24 = 624
2. 8 × 23 → 8(20 + 3) = 160 + 24 = 184
3. 14 × 102 → 14(100 + 2) = 1400 + 28 = 1428
4. 5 × 312 → 5(300 + 10 + 2) = 1500 + 50 + 10 = 1560

Part 2
5. 4 × 98 → 4(100 - 2) = 400 - 8 = 392
6. 9 × 39 → 9(40 - 1) = 360 - 9 = 351
7. 12 × 99 → 12(100 - 1) = 1200 - 12 = 1188
8. 6 × 195 → 6(200 - 5) = 1200 - 30 = 1170