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Evaluate the following using properties ...

Evaluate the following using properties for multiplication to simplify the multiplication.
`(-59) times 102`

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To evaluate the expression \((-59) \times 102\) using properties of multiplication, we can follow these steps: ### Step-by-Step Solution: 1. **Rewrite the Expression**: We can express \(102\) as \(100 + 2\). Thus, we rewrite the expression: \[ (-59) \times 102 = (-59) \times (100 + 2) \] 2. **Apply the Distributive Property**: Using the distributive property, we can distribute \(-59\) across the sum: \[ (-59) \times (100 + 2) = (-59) \times 100 + (-59) \times 2 \] 3. **Calculate Each Term**: - First, calculate \((-59) \times 100\): \[ (-59) \times 100 = -5900 \] - Next, calculate \((-59) \times 2\): \[ (-59) \times 2 = -118 \] 4. **Combine the Results**: Now we combine the results from the two calculations: \[ -5900 + (-118) = -5900 - 118 \] To perform this addition, we can calculate: \[ -5900 - 118 = -5918 \] 5. **Final Answer**: Therefore, the result of \((-59) \times 102\) is: \[ \boxed{-5918} \]
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