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Solve, using properties/ methods that si...

Solve, using properties/ methods that simplify the calculations:
`398xx9999`

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To solve the problem \( 398 \times 9999 \) using properties that simplify calculations, we can follow these steps: ### Step-by-Step Solution: 1. **Rewrite the Numbers**: - We can express \( 398 \) as \( 400 - 2 \). - We can express \( 9999 \) as \( 10,000 - 1 \). - So, we rewrite the expression: \[ 398 \times 9999 = (400 - 2) \times (10,000 - 1) \] 2. **Apply the Distributive Property**: - According to the distributive property, \( A \times (B - C) = A \times B - A \times C \). - We can apply this property: \[ (400 - 2) \times (10,000 - 1) = 400 \times 10,000 - 400 \times 1 - 2 \times 10,000 + 2 \times 1 \] 3. **Calculate Each Part**: - Now, we calculate each term: - \( 400 \times 10,000 = 4,000,000 \) - \( 400 \times 1 = 400 \) - \( 2 \times 10,000 = 20,000 \) - \( 2 \times 1 = 2 \) 4. **Combine the Results**: - Now, substitute the calculated values back into the expression: \[ 4,000,000 - 400 - 20,000 + 2 \] 5. **Perform the Final Calculation**: - First, subtract \( 400 \) from \( 4,000,000 \): \[ 4,000,000 - 400 = 3,999,600 \] - Next, subtract \( 20,000 \): \[ 3,999,600 - 20,000 = 3,979,600 \] - Finally, add \( 2 \): \[ 3,979,600 + 2 = 3,979,602 \] ### Final Answer: Thus, the solution to \( 398 \times 9999 \) is: \[ \boxed{3,979,602} \]
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