Let's evaluate each statement one by one.
Statement #1: \( 3 \cdot 20 = 4(6 + 9) \)
Calculating each side:
Left Side: \[ 3 \cdot 20 = 60 \]
Right Side: \[ 4(6 + 9) = 4 \cdot 15 = 60 \]
Both sides are equal, so Statement #1 is true.
Statement #2: \( 4 \times 12 = 6 \times (8 \times 2) , 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8 \)
Calculating each part:
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\( 4 \times 12 \): \[ 4 \times 12 = 48 \]
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\( 6 \times (8 \times 2) \): \[ 8 \times 2 = 16 \quad \text{then} \quad 6 \times 16 = 96 \] So, \( 6 \times (8 \times 2) = 96 \).
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The expression after \( = \): \[ 12 + 6 \cdot \sqrt{64} = 12 + 6 \cdot 8 = 12 + 48 = 60 \] Therefore, the equality written in the statement seems to have some misunderstanding as it mixes some parts incorrectly without proper operations.
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\( 2 \cdot 4 \cdot 8 \): \[ 2 \cdot 4 \cdot 8 = 64 \]
Putting these together for Statement #2, we have: \[ 4 \times 12 = 48 \quad \text{(Left Side)}, \quad 6 \times (8 \times 2) + 12 + 6 \cdot \sqrt{64} = 96 + 60 = 156 \quad \text{(Right Side)} \] This statement is false.
Statement #3: \( 4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8 \)
Calculating each side:
Left Side: \[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]
Right Side: \[ 42 + 4 \cdot 8 = 42 + 32 = 74 \]
So, this results in: \[ 48 \neq 74 \] Thus, Statement #3 is false.
Summary
From the evaluations:
- Statement #1 is true.
- Statement #2 is false.
- Statement #3 is false.
Therefore, the only correct statement is:
1.