What is the value of `[ 75 -: 25 "of " ( (4)/(3) - (1)/(2) + (1)/(6))]` ?

Options

A. `(5)/(6)`
B. 3
C. `(7)/(6)`
D. 5

Answer

To solve the expression \( 75 \div 25 \text{ of } \left( \frac{4}{3} - \frac{1}{2} + \frac{1}{6} \right) \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate the expression inside the brackets:**
\[ \frac{4}{3} - \frac{1}{2} + \frac{1}{6} \]
To perform this calculation, we need a common denominator. The least common multiple of 3, 2, and 6 is 6.

- Convert \(\frac{4}{3}\) to sixths:
\[ \frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6} \]
- Convert \(\frac{1}{2}\) to sixths:
\[ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \]
- \(\frac{1}{6}\) is already in sixths.

Now substitute back into the expression:
\[ \frac{8}{6} - \frac{3}{6} + \frac{1}{6} \]
Combine the fractions:
\[ \frac{8 - 3 + 1}{6} = \frac{6}{6} = 1 \]

2. **Substitute back into the original expression:**
Now we have:
\[ 75 \div 25 \text{ of } 1 \]

3. **Calculate \(75 \div 25\):**
\[ 75 \div 25 = 3 \]

4. **Multiply by 1:**
\[ 3 \text{ of } 1 = 3 \]

### Final Answer:
The value of the expression is \(3\).