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Which expression is equivalent to [tex]$3 \times (6+9)$[/tex]?

A. [tex]$(3+6)+(3+9)$[/tex]

B. [tex]$(3 \times 6)+(3+9)$[/tex]

C. [tex][tex]$(3+6)+(3 \times 9)$[/tex][/tex]

D. [tex]$(3 \times 6)+(3 \times 9)$[/tex]

Sagot :

GinnyAnswer
Certainly! Let’s analyze and compare each option to find which expression is equivalent to [tex]\(3 \times (6 + 9)\)[/tex].

First, let's compute the value of the given expression:
[tex]\[3 \times (6 + 9).\][/tex]

Step 1: Compute the value inside the parentheses:
[tex]\[6 + 9 = 15.\][/tex]

Step 2: Multiply the result by 3:
[tex]\[3 \times 15 = 45.\][/tex]

Now, we'll evaluate each of the given options to see which one equals 45.

### Option A: [tex]\((3 + 6) + (3 + 9)\)[/tex]

Step 1: Compute the values inside the parentheses:
[tex]\[3 + 6 = 9\][/tex]
[tex]\[3 + 9 = 12\][/tex]

Step 2: Add the two results:
[tex]\[9 + 12 = 21\][/tex]

So, option A evaluates to 21, which is not equal to 45.

### Option B: [tex]\((3 \times 6) + (3 + 9)\)[/tex]

Step 1: Compute the values inside the parentheses:
[tex]\[3 \times 6 = 18\][/tex]
[tex]\[3 + 9 = 12\][/tex]

Step 2: Add the two results:
[tex]\[18 + 12 = 30\][/tex]

So, option B evaluates to 30, which is not equal to 45.

### Option C: [tex]\((3 + 6) + (3 \times 9)\)[/tex]

Step 1: Compute the values inside the parentheses:
[tex]\[3 + 6 = 9\][/tex]
[tex]\[3 \times 9 = 27\][/tex]

Step 2: Add the two results:
[tex]\[9 + 27 = 36\][/tex]

So, option C evaluates to 36, which is not equal to 45.

### Option D: [tex]\((3 \times 6) + (3 \times 9)\)[/tex]

Step 1: Compute the values inside the parentheses:
[tex]\[3 \times 6 = 18\][/tex]
[tex]\[3 \times 9 = 27\][/tex]

Step 2: Add the two results:
[tex]\[18 + 27 = 45\][/tex]

So, option D evaluates to 45, which is equal to 45.

Hence, the expression that is equivalent to [tex]\(3 \times (6 + 9)\)[/tex] is:

D. [tex]\((3 \times 6) + (3 \times 9)\)[/tex]
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