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Evaluate: 32.5 + 12 . 43 xx 0.2 + 16.6...

Evaluate:
`32.5 + 12 . 43 xx 0.2 + 16.6 div 0.02 - 4. 07`

Text Solution

AI Generated Solution

The correct Answer is:
To evaluate the expression `32.5 + 12.43 * 0.2 + 16.6 ÷ 0.02 - 4.07`, we will follow the order of operations, often referred to as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). ### Step-by-Step Solution: 1. **Identify the operations**: The expression consists of addition, multiplication, division, and subtraction. According to BODMAS, we perform division and multiplication before addition and subtraction. 2. **Perform the division**: \[ 16.6 \div 0.02 \] To divide, we can convert it into a fraction: \[ 16.6 = \frac{166}{10}, \quad 0.02 = \frac{2}{100} \] Thus, \[ 16.6 \div 0.02 = \frac{166}{10} \times \frac{100}{2} = \frac{166 \times 100}{10 \times 2} = \frac{16600}{20} = 830 \] 3. **Perform the multiplication**: \[ 12.43 \times 0.2 \] To multiply, we can do: \[ 12.43 \times 0.2 = 12.43 \times \frac{2}{10} = \frac{12.43 \times 2}{10} = \frac{24.86}{10} = 2.486 \] 4. **Substitute back into the expression**: Now we can replace the division and multiplication results back into the expression: \[ 32.5 + 2.486 + 830 - 4.07 \] 5. **Perform the addition**: First, add \(32.5\) and \(2.486\): \[ 32.5 + 2.486 = 34.986 \] Now add \(34.986\) and \(830\): \[ 34.986 + 830 = 864.986 \] 6. **Perform the subtraction**: Finally, subtract \(4.07\) from \(864.986\): \[ 864.986 - 4.07 = 860.916 \] ### Final Answer: The evaluated result of the expression is: \[ \boxed{860.916} \]
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