Simplify $8 \div 4 \times 2+\left(7^2-3+5\right)$
Answer (2)
Simplify the expression inside the parentheses: 7 2 − 3 + 5 = 49 − 3 + 5 = 51 .
Perform the division and multiplication from left to right: 8 d i v 4 t im es 2 = 2 t im es 2 = 4 .
Add the results: 4 + 51 = 55 .
The simplified expression is 55 .
Explanation
Understanding the Expression We need to simplify the expression 8 d i v 4 t im es 2 + ( 7 2 − 3 + 5 ) . To do this, we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Simplifying Parentheses First, we simplify the expression inside the parentheses: 7 2 − 3 + 5 . We start with the exponent: 7 2 = 49 . Then, we perform the subtraction and addition from left to right: 49 − 3 + 5 = 46 + 5 = 51 .
Performing Division and Multiplication Next, we deal with the division and multiplication. We have 8 d i v 4 t im es 2 . We perform these operations from left to right. First, 8 d i v 4 = 2 . Then, 2 t im es 2 = 4 .
Adding the Results Finally, we perform the addition. We have 4 + 51 = 55 .
Final Answer Therefore, the simplified expression is 55 .
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating expenses or determining the outcome of a series of events. For example, if you are calculating the total cost of items with discounts and taxes, following the correct order ensures you get the accurate final amount. Similarly, in programming, the order of operations determines how expressions are evaluated, which can affect the program's output. Correctly applying PEMDAS helps avoid errors and ensures accurate results in various calculations.
To simplify the expression 8 ÷ 4 × 2 + ( 7 2 − 3 + 5 ) , we first evaluate the parentheses to get 51. Then, we perform the division and multiplication to get 4. Lastly, we add the results, yielding the final answer of 55.
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