Determine which of the following statements is/are true:

#1: 3 x 20 = 4(6 + 9)
#2: 4 x 12 = 6 x (8 x 2) 12 + 6 x square root 64 = 2 x 4 x 8
#3: 4 x 18 - 4 x 6 = 4^2 + 4 x 8

1
2 and 3
1 and 3
1 and 2

1 answer

Let's evaluate each statement one by one:

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

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

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

So, statement #1 is true.


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 \( 6 \times (8 \times 2) \): \[ 8 \times 2 = 16 \] \[ 6 \times 16 = 96 \]

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

Now, combining both: \[ 96 + 48 = 144 \]

Finally, check the rightmost part: \[ 2 \times 4 \times 8 = 64 \]

Since \( 48 \neq 144 \), statement #2 is false.


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: \[ 4^2 = 16 \] \[ 4 \times 8 = 32 \] Thus, \[ 16 + 32 = 48 \]

Since both sides are equal, statement #3 is true.


In summary:

  • Statement #1: True
  • Statement #2: False
  • Statement #3: True

So the true statements are #1 and #3.

The correct answer is 1 and 3.