Technique explanation
Teaching Explanation
In math, a "Friendly Base" is a power of 10 (10, 100, 1000) that makes our calculations simpler. When we multiply numbers like 98 and 97, using Base 100 is "friendly" because the differences (2 and 3) are small. If we used Base 10, the differences would be huge (88 and 87), which isn't helpful. Choosing the right base is like picking the right tool for a job—it doesn't change the answer, but it changes how much work you have to do.
Method Condition
Applied when preparing for near-base strategies.
Standard Fallback
Always default to Base 10 if unsure, or use standard multiplication if the number is not close to any power of 10.
Misconception & Correction
Misconception: Thinking you must* use the nearest base even if the standard method is faster.
- Correction: The "Friendly Base" is a strategy, not a rule. If the differences are still large (e.g., 65 and 67 from Base 100), the standard method or crosswise multiplication may be more efficient.
Worked examples
Worked Examples
Example: Identify the best base for 997 × 998
- Compare: Is it closer to 100 or 1000?
- Distance to 100: ~900 units.
- Distance to 1000: 3 and 2 units.
- Selection: Base 1000.
- Independent Check: A smaller difference (3 vs 900) results in simpler multiplication (3×2 vs 900×897).
Example: Identify the best base for 12 × 13
- Compare: Is it closer to 10 or 100?
- Distance to 10: 2 and 3 units.
- Distance to 100: 88 and 87 units.
- Selection: Base 10.
- Independent Check: Differences of 2 and 3 are easier to manage than 88 and 87.
Academy Course