Question

Determine which of the following statements is/are true:
#1: 3 * 20 = 4(6 + 9)
#2: 4 * 12 = 6 * (8 * 2) 12 + 6 * √64 = 2 * 4 * 8
#3: 4 * 18 – 4 * 6 = 4^2 + 4 * 8

Answer 1

Let's evaluate each of the statements one by one.

**Statement #1:**
\( 3 \times 20 = 4(6 + 9) \)

Calculating the left side:
\[ 3 \times 20 = 60 \]

Calculating the right side:
\[ 4(6 + 9) = 4 \times 15 = 60 \]

Since both sides equal 60, **Statement #1 is true.**

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**Statement #2:**
\[ 4 \times 12 = 6 \times (8 \times 2) + 6 \times \sqrt{64} = 2 \times 4 \times 8 \]

Calculating the left side:
\[ 4 \times 12 = 48 \]

Calculating the right side:
First, calculate \( 8 \times 2 \):
\[ 8 \times 2 = 16 \]
Then,
\[ 6 \times 16 = 96 \]

Now calculate \( \sqrt{64} \):
\[ \sqrt{64} = 8 \]
Thus,
\[ 6 \times 8 = 48 \]

Now add:
\[ 96 + 48 = 144 \]

Now check the equation:
The left side is \( 48 \), and the right side is \( 144 \). So,
\[ 48 \neq 144 \]

Thus, **Statement #2 is false.**

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**Statement #3:**
\[ 4 \times 18 - 4 \times 6 = 4^2 + 4 \times 8 \]

Calculating the left side:
\[ 4 \times 18 = 72 \]
\[ 4 \times 6 = 24 \]
Thus:
\[ 72 - 24 = 48 \]

Calculating the right side:
\[ 4^2 = 16 \]
\[ 4 \times 8 = 32 \]
Adding these gives:
\[ 16 + 32 = 48 \]

Since both sides equal 48, **Statement #3 is true.**

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**Final Summary:**
- Statement #1 is true.
- Statement #2 is false.
- Statement #3 is true.