Certainly! Let's solve these mathematical expressions step by step.
### Part (a): \((50 - 5 \times 4) \div (2 + 36 \times 9)\)
1. Calculate the numerator:
- First, perform the multiplication within the numerator: \(5 \times 4 = 20\).
- Then, subtract from 50: \(50 - 20 = 30\).
2. Calculate the denominator:
- First, perform the multiplication within the denominator: \(36 \times 9 = 324\).
- Then, add 2 to the result: \(2 + 324 = 326\).
3. Perform the division:
- Divide the numerator by the denominator: \(\frac{30}{326} \approx 0.09202453987730061\).
### Part (b): \(63 \div \{(5 + 3) \times 4 - 23\}\)
1. Simplify the expression inside the curly braces:
- First, evaluate the sum inside the parentheses: \(5 + 3 = 8\).
- Then, perform the multiplication: \(8 \times 4 = 32\).
- Finally, subtract 23 from the result: \(32 - 23 = 9\).
2. Perform the division:
- Divide 63 by the result of the simplified expression: \(\frac{63}{9} = 7\).
### Part (d): \(8 + 12 \times \{(9 - 7) + 3\}\)
1. Simplify the expression inside the curly braces:
- First, evaluate the subtraction inside the parentheses: \(9 - 7 = 2\).
- Then, add 3 to the result: \(2 + 3 = 5\).
2. Perform the multiplication:
- Multiply 12 by the result of the simplified expression: \(12 \times 5 = 60\).
3. Add the result to 8:
- Finally, add 8 to the product: \(8 + 60 = 68\).
So the results for each part are:
- Part (a): \((50 - 5 \times 4) \div (2 + 36 \times 9) \approx 0.09202453987730061\)
- Part (b): \(63 \div \{(5 + 3) \times 4 - 23\} = 7\)
- Part (d): [tex]\(8 + 12 \times \{(9 - 7) + 3\} = 68\)[/tex]
