Technique explanation
Teaching Explanation
When multiplying numbers like 97 and 96, we can use their proximity to 100 to simplify the work. We first find the deficiency of each number (how much it is below 100). For 97, the deficiency is -3; for 96, it is -4. The answer has two parts: the left side is found by cross-subtracting one deficiency from the other number ($97 - 4 = 93$), and the right side is the product of the deficiencies ($-3 \times -4 = 12$). Combined, they give 9312.
Method Conditions
Both numbers must be close to and below the base 100 (typically 90–99).
Standard Fallback
Standard long multiplication.
Misconception & Correction
Misconception: Adding the deficiencies for the right-hand side instead of multiplying them.
Correction: The right-hand side represents the product of the differences from the base ($d_1 \times d_2$).
Module
Worked examples
Worked Examples
- Calculate $97 \times 96$. Step 1: Deficiencies are -3 and -4. Step 2: Left side: $97 - 4 = 93$ (or $96 - 3 = 93$). Step 3: Right side: $-3 \times -4 = 12$. Result: 9312. Verification: $97 \times 96 = 9312$.
- Calculate $98 \times 91$. Step 1: Deficiencies are -2 and -9. Step 2: Left side: $98 - 9 = 89$ (or $91 - 2 = 89$). Step 3: Right side: $-2 \times -9 = 18$. Result: 8918. Verification: $98 \times 91 = 8918$.
Academy Course
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