Find the value of `5(1)/(2) - [3(1)/(4) + 6 - 4 div 2]`

Options

A. `-(5)/(4)`
B. `(5)/(4)`
C. `(7)/(4)`
D. `-(7)/(4)`

Answer

To solve the expression \(5\frac{1}{2} - \left[3\frac{1}{4} + 6 - 4 \div 2\right]\), we will follow the order of operations (BODMAS/BIDMAS). Let's break it down step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions
Convert \(5\frac{1}{2}\) and \(3\frac{1}{4}\) into improper fractions.

- \(5\frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}\)
- \(3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}\)

### Step 2: Rewrite the Expression
Now, rewrite the expression using the improper fractions:
\[ \frac{11}{2} - \left[\frac{13}{4} + 6 - 4 \div 2\right] \]

### Step 3: Solve the Division Inside the Bracket
Calculate \(4 \div 2\):
\[ 4 \div 2 = 2 \]

### Step 4: Substitute Back into the Expression
Now substitute back into the expression:
\[ \frac{11}{2} - \left[\frac{13}{4} + 6 - 2\right] \]

### Step 5: Simplify Inside the Bracket
Now simplify the expression inside the bracket:
\[ 6 - 2 = 4 \]
So, we have:
\[ \frac{11}{2} - \left[\frac{13}{4} + 4\right] \]

### Step 6: Convert 4 to a Fraction
Convert 4 into a fraction with a denominator of 4:
\[ 4 = \frac{4 \times 4}{4} = \frac{16}{4} \]

### Step 7: Add the Fractions Inside the Bracket
Now we can add the fractions inside the bracket:
\[ \frac{13}{4} + \frac{16}{4} = \frac{29}{4} \]

### Step 8: Substitute Back into the Expression
Now substitute this back into the expression:
\[ \frac{11}{2} - \frac{29}{4} \]

### Step 9: Find a Common Denominator
To subtract these fractions, we need a common denominator. The least common multiple of 2 and 4 is 4. Convert \(\frac{11}{2}\) to a fraction with a denominator of 4:
\[ \frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4} \]

### Step 10: Subtract the Fractions
Now we can subtract:
\[ \frac{22}{4} - \frac{29}{4} = \frac{22 - 29}{4} = \frac{-7}{4} \]

### Final Answer
The value of the expression is:
\[ \frac{-7}{4} \]

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