1.2.7 Multiplying Two Numbers Near 100
This trick allows you to quickly multiply numbers that are close to 100 (or 1000, 10000, etc.).
Case 1: Both Numbers Above 100
Express n₁ = (100 + a) and n₂ = (100 + b), then:
n₁ × n₂ = 100(n₁ + b) + ab = 100(n₂ + a) + ab
Example: 103 × 108
| Step | Calculation | Result |
|---|---|---|
| Tens/Ones | 3 × 8 | 24 |
| Rest of Answer | 103 + 8 (or 108 + 3) | 111 |
Answer: 11124
Case 2: Both Numbers Below 100
Express n₁ = (100 − a) and n₂ = (100 − b), then:
n₁ × n₂ = 100(n₁ − b) + ab = 100(n₂ − a) + ab
Example: 97 × 94
| Step | Calculation | Result |
|---|---|---|
| Tens/Ones | 3 × 6 | 18 |
| Rest of Answer | 97 − 6 (or 94 − 3) | 91 |
Answer: 9118
Case 3: One Above, One Below 100
This case is trickier. Let n₁ be above 100 and n₂ be below 100:
Example: 103 × 94
| Step | Calculation | Result |
|---|---|---|
| Tens/Ones | 100 − (3 × 6) | 82 |
| Rest of Answer | 103 − 6 − 1 | 96 |
Answer: 9682
Example: 108 × 93
| Step | Calculation | Result |
|---|---|---|
| Tens/Ones | 100 − (8 × 7) | 44 |
| Rest of Answer | 108 − 7 − 1 | 100 |
Answer: 10044
Tip: For one above/one below: subtract the product from 100 for the last two digits, and subtract an extra 1 from the first part.
Extension to 1000 and Beyond
The trick extends to numbers near 1000, 10000, etc. Just remember to pad with zeros!
Example: 1002 × 1007
| Step | Calculation | Result |
|---|---|---|
| Last 3 digits | 2 × 7 | 014 |
| Rest of Answer | 1002 + 7 | 1009 |
Answer: 1009014
Example: 993 × 994
| Step | Calculation | Result |
|---|---|---|
| Last 3 digits | 7 × 6 | 042 |
| Rest of Answer | 993 − 6 | 987 |
Answer: 987042
Tip: For numbers near 1000, expect a 6-7 digit answer. The “rest” gives you 4 digits, so pad the product to 3 digits.
Problem Set 1.2.7
Practice these problems. Type your answer and press Enter to check: