Determine which of the following statements is/are true:

Question

#1: 3⋅20=4(6+9)

#2: 4×12=6×(8×2)12+6⋅64−−√=2⋅4⋅8

#3: 4⋅18−4⋅6=42+4⋅8

(1 point)
Responses

1
1

1 and 2
1 and 2

1 and 3
1 and 3

2 and 3

Answer 1

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: \( 4(6 + 9) = 4 \cdot 15 = 60 \)

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

Statement #2:

\[ 4 \times 12 = 6 \times (8 \times 2) \] Calculating each side:

• Left side: \( 4 \times 12 = 48 \)
• Right side: \( 6 \times (8 \times 2) = 6 \times 16 = 96 \)

The left side is 48 and the right side is 96, so Statement #2 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: \( 42 + 4 \cdot 8 = 42 + 32 = 74 \)

The left side is 48 and the right side is 74, so Statement #3 is false.

Summary of evaluations:

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

The only true statement is Statement #1. Thus, the correct response is:

1