23 x 27 - (12 x 15 ÷ 2) - [ (23 + 5) x (27 - 12 ÷ 2) ]
Understand the Problem
The question involves simplifying a mathematical expression with multiple operations, including multiplication, division, and parentheses. It requires applying the order of operations to arrive at a single numerical result.
Answer
The simplified value of the expression is $-57$.
Answer for screen readers
The final result of the expression is $-57$.
Steps to Solve
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Calculate the first multiplication Calculate $23 \times 27$. $$ 23 \times 27 = 621 $$
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Calculate the expression in the first parentheses Calculate $12 \times 15 \div 2$. First, calculate $12 \times 15$, then divide by 2. $$ 12 \times 15 = 180 $$ $$ 180 \div 2 = 90 $$
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Calculate the expression in the second parentheses Calculate $23 + 5$ and $27 - 12 \div 2$. First, calculate $12 \div 2$. $$ 12 \div 2 = 6 $$ Now, calculate $27 - 6$. $$ 27 - 6 = 21 $$ Now calculate $23 + 5$. $$ 23 + 5 = 28 $$ Now multiply these results: $$ 28 \times 21 = 588 $$
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Combine all parts of the expression Now, combine all parts of the expression: $$ 621 - 90 - 588 $$ Calculate $621 - 90$: $$ 621 - 90 = 531 $$ Now, calculate $531 - 588$: $$ 531 - 588 = -57 $$
The final result of the expression is $-57$.
More Information
The expression involves multiple arithmetic operations, including multiplication, division, and addition/subtraction. It's essential to follow the order of operations (PEMDAS/BODMAS) to simplify correctly.
Tips
- Not following the order of operations can lead to incorrect results. Always do calculations inside parentheses first, and then perform multiplications/divisions before additions/subtractions.
- Forgetting to divide correctly when multiple operations are present can also result in mistakes.
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