Apply the rules for order of operations to simplify $2+3-4+(5 \times 4)$.
A. 22
B. 9
C. 21
D. 24
Answer (2)
Multiply within the parentheses: 5 × 4 = 20 .
Perform addition and subtraction from left to right: 2 + 3 − 4 + 20 = 5 − 4 + 20 = 1 + 20 .
Add the remaining numbers: 1 + 20 = 21 .
The simplified expression is 21 .
Explanation
Understanding the Order of Operations We need to simplify the expression 2 + 3 − 4 + ( 5 × 4 ) using the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This tells us the sequence in which we should perform the operations.
Performing Multiplication First, we look for any parentheses. Inside the parentheses, we have a multiplication operation: 5 × 4 = 20 . So, we replace ( 5 × 4 ) with 20 in the original expression.
Addition and Subtraction (Left to Right) Now our expression looks like this: 2 + 3 − 4 + 20 . We perform addition and subtraction from left to right. First, we add 2 + 3 , which equals 5 .
Continuing Addition and Subtraction Now our expression is 5 − 4 + 20 . Next, we subtract 4 from 5 , which equals 1 .
Final Addition Finally, we have 1 + 20 , which equals 21 . Therefore, the simplified expression is 21 .
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating expenses or managing budgets. For instance, if you're buying items at a store with discounts and taxes, you need to apply the discount first (multiplication), then add the tax (addition) to get the correct final amount. Similarly, in cooking, following the correct order of steps ensures the dish turns out as expected. This principle extends to more complex calculations in finance, engineering, and computer programming, where the correct sequence of operations is essential for accurate results.
The simplified value of the expression 2 + 3 − 4 + ( 5 × 4 ) is 21 . This was determined by first performing the multiplication, followed by addition and subtraction from left to right. Hence, the correct answer is option C: 21.
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