`(48-12xx3+9)/(12-9div3)=?`

Options

A. 3
B. 21
C. (7/3)
D. (1/3)

Answer

To solve the expression \((48 - 12 \times 3 + 9) / (12 - 9 \div 3)\), we will follow the order of operations (BODMAS/BIDMAS rules: Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).

### Step 1: Solve the numerator
The numerator is \(48 - 12 \times 3 + 9\).

1. Calculate \(12 \times 3\):
\[ 12 \times 3 = 36 \]
Now, substitute this back into the numerator:
\[ 48 - 36 + 9 \]

2. Perform the subtraction:
\[ 48 - 36 = 12 \]
Now, substitute this back:
\[ 12 + 9 \]

3. Finally, perform the addition:
\[ 12 + 9 = 21 \]

So, the numerator simplifies to \(21\).

### Step 2: Solve the denominator
The denominator is \(12 - 9 \div 3\).

1. Calculate \(9 \div 3\):
\[ 9 \div 3 = 3 \]
Now, substitute this back into the denominator:
\[ 12 - 3 \]

2. Perform the subtraction:
\[ 12 - 3 = 9 \]

So, the denominator simplifies to \(9\).

### Step 3: Combine the results
Now we have:
\[ \frac{21}{9} \]

### Step 4: Simplify the fraction
To simplify \(\frac{21}{9}\), we can divide both the numerator and the denominator by their greatest common divisor, which is \(3\):
\[ \frac{21 \div 3}{9 \div 3} = \frac{7}{3} \]

### Final Answer
Thus, the final answer is:
\[ \frac{7}{3} \]

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