Simplify the given expression:
`(2 (3)/(4) xx 432 - 50 % of 1342 div {1-(4(3)/(9) + (2)/(9) - 4 (5)/(9))})/(2 xx 4-1 + 3 xx 50 % of 340)`

Options

A. 1
B. 4
C. 2
D. 6

Answer

To simplify the given expression step by step, we will follow the order of operations (BODMAS/BIDMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Given Expression:
\[ \frac{2 \frac{3}{4} \times 432 - 50\% \text{ of } 1342}{1 - \left(4 \frac{3}{9} + \frac{2}{9} - 4 \frac{5}{9}\right)} \div \left(2 \times 4 - 1 + 3 \times 50\% \text{ of } 340\right) \]

### Step 1: Convert Mixed Numbers and Percentages
Convert the mixed numbers and calculate the percentages:
- \(2 \frac{3}{4} = \frac{11}{4}\)
- \(50\% \text{ of } 1342 = \frac{1342}{2} = 671\)
- \(50\% \text{ of } 340 = \frac{340}{2} = 170\)

### Step 2: Substitute Values
Substituting the values back into the expression:
\[ \frac{\frac{11}{4} \times 432 - 671}{1 - \left(4 \frac{3}{9} + \frac{2}{9} - 4 \frac{5}{9}\right)} \div \left(2 \times 4 - 1 + 510\right) \]

### Step 3: Simplify the Denominator
Calculate the expression inside the brackets:
- \(4 \frac{3}{9} = \frac{39}{9}\)
- \(\frac{2}{9} = \frac{2}{9}\)
- \(4 \frac{5}{9} = \frac{41}{9}\)

Now, combine these:
\[ 1 - \left(\frac{39}{9} + \frac{2}{9} - \frac{41}{9}\right) = 1 - \left(\frac{39 + 2 - 41}{9}\right) = 1 - \left(\frac{0}{9}\right) = 1 \]

### Step 4: Simplify the Other Denominator
Calculate:
\[ 2 \times 4 - 1 + 510 = 8 - 1 + 510 = 517 \]

### Step 5: Substitute Back
Now substitute these values back into the expression:
\[ \frac{\frac{11}{4} \times 432 - 671}{1} \div 517 \]

### Step 6: Calculate the Numerator
Calculate \(\frac{11}{4} \times 432\):
\[ \frac{11 \times 432}{4} = \frac{4752}{4} = 1188 \]
Now substitute this back:
\[ \frac{1188 - 671}{1} = 517 \]

### Step 7: Final Calculation
Now divide by 517:
\[ \frac{517}{517} = 1 \]

### Final Answer:
The simplified expression equals \(1\).

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