What is the value of `512 div 16 + 4 xx (5)/(2) " of " ((1)/(8) +(1)/(3))`?

Options

A. `(455)/(12)`
B. `(449)/(12)`
C. `(439)/(12)`
D. `(443)/(12)`

Answer

To solve the expression \( 512 \div 16 + 4 \times \left( \frac{5}{2} \right) \text{ of } \left( \frac{1}{8} + \frac{1}{3} \right) \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Evaluate the expression inside the brackets:**
\[ \frac{1}{8} + \frac{1}{3} \]
To add these fractions, we need a common denominator. The least common multiple of 8 and 3 is 24.
\[ \frac{1}{8} = \frac{3}{24}, \quad \frac{1}{3} = \frac{8}{24} \]
Therefore,
\[ \frac{1}{8} + \frac{1}{3} = \frac{3}{24} + \frac{8}{24} = \frac{11}{24} \]

**Hint:** Find a common denominator to add fractions.

2. **Substitute back into the expression:**
Now, substitute \( \frac{11}{24} \) back into the expression:
\[ 512 \div 16 + 4 \times \left( \frac{5}{2} \right) \times \frac{11}{24} \]

3. **Perform the division:**
\[ 512 \div 16 = 32 \]

**Hint:** Division is performed before addition.

4. **Calculate the multiplication:**
First, calculate \( 4 \times \frac{5}{2} \):
\[ 4 \times \frac{5}{2} = \frac{20}{2} = 10 \]
Now multiply this result by \( \frac{11}{24} \):
\[ 10 \times \frac{11}{24} = \frac{110}{24} \]

**Hint:** Multiply the whole number by the fraction.

5. **Simplify \( \frac{110}{24} \):**
Divide both the numerator and denominator by their greatest common divisor (GCD), which is 2:
\[ \frac{110 \div 2}{24 \div 2} = \frac{55}{12} \]

**Hint:** Always simplify fractions when possible.

6. **Add the results:**
Now we add \( 32 \) and \( \frac{55}{12} \):
Convert \( 32 \) to a fraction with a denominator of 12:
\[ 32 = \frac{384}{12} \]
Now add:
\[ \frac{384}{12} + \frac{55}{12} = \frac{384 + 55}{12} = \frac{439}{12} \]

**Hint:** Convert whole numbers to fractions with a common denominator before adding.

### Final Answer:
The value of the expression is \( \frac{439}{12} \).