Simplify $6+8 \div 2 \times|-3|+7$.
Answer (2)
Evaluate the absolute value: ∣ − 3∣ = 3 .
Perform the division: 8 ÷ 2 = 4 .
Perform the multiplication: 4 × 3 = 12 .
Perform the additions: 6 + 12 + 7 = 25 . The simplified expression is 25 .
Explanation
Understanding the Expression We need to simplify the expression 6 + 8 ÷ 2 × ∣ − 3∣ + 7 . To do this, we will follow the order of operations (PEMDAS/BODMAS), which tells us to evaluate Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Evaluating the Absolute Value First, we evaluate the absolute value: ∣ − 3∣ = 3 . So the expression becomes 6 + 8 ÷ 2 × 3 + 7 .
Performing the Division Next, we perform the division: 8 ÷ 2 = 4 . The expression becomes 6 + 4 × 3 + 7 .
Performing the Multiplication Now, we perform the multiplication: 4 × 3 = 12 . The expression becomes 6 + 12 + 7 .
Performing the Additions Finally, we perform the additions from left to right: 6 + 12 = 18 , and then 18 + 7 = 25 .
Final Answer Therefore, the simplified expression is 25.
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 actions. For example, if you earn $6 per hour and work 8 hours, but have to spend $2 on transportation each day for 3 days, the total earnings can be calculated as 6 + ( 8 ÷ 1 ) × 6 − 2 × 3 = 42 . This demonstrates how following the correct order of operations ensures accurate financial calculations.
The expression 6 + 8 ÷ 2 × ∣ − 3∣ + 7 simplifies to 25 by following the order of operations, evaluating the absolute value first, then performing division, multiplication, and finally addition. Each operation follows the correct sequence to arrive at the final answer. The answer is 25 .
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