Find the value of 309 `div [(3/2)` of `(25+35)-123/4]`

Options

A. 4
B. 16
C. 12
D. 8

Answer

To solve the problem, we need to evaluate the expression step by step. The expression we need to simplify is:

\[ 309 \div \left[ \left( \frac{3}{2} \right) \text{ of } (25 + 35) - \frac{123}{4} \right] \]

### Step 1: Calculate \( 25 + 35 \)
First, we add \( 25 \) and \( 35 \):

\[ 25 + 35 = 60 \]

**Hint:** Always start by simplifying expressions inside the parentheses.

### Step 2: Calculate \( \frac{3}{2} \text{ of } 60 \)
Next, we find \( \frac{3}{2} \) of \( 60 \):

\[ \frac{3}{2} \times 60 = \frac{180}{2} = 90 \]

**Hint:** To find "of" in a mathematical context, multiply the fraction by the number.

### Step 3: Calculate \( \frac{123}{4} \)
Now, we calculate \( \frac{123}{4} \):

\[ \frac{123}{4} = 30.75 \]

**Hint:** Dividing a number by 4 can be done by either long division or converting to a decimal.

### Step 4: Substitute and simplify the expression
Now we substitute back into the expression:

\[ 90 - 30.75 = 59.25 \]

**Hint:** When subtracting, ensure to align decimal points for accuracy.

### Step 5: Calculate \( 309 \div 59.25 \)
Now we perform the division:

\[ 309 \div 59.25 \]

To make the division easier, we can convert \( 59.25 \) to a fraction:

\[ 59.25 = \frac{5925}{100} = \frac{237}{4} \]

So, we can rewrite the division as:

\[ 309 \div \left( \frac{237}{4} \right) = 309 \times \left( \frac{4}{237} \right) \]

### Step 6: Calculate \( 309 \times \frac{4}{237} \)
Now we multiply:

\[ 309 \times 4 = 1236 \]

Now divide \( 1236 \) by \( 237 \):

\[ 1236 \div 237 = 5.2 \]

**Hint:** When multiplying fractions, multiply the numerators and denominators separately.

### Final Answer
Thus, the value of the expression is:

\[ \boxed{5.2} \]