Solve The Problem Below.$\[3 \times 10 + 8 \div 2 - (3 + 5)\\]
Introduction
In mathematics, solving problems often involves following the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. In this article, we will use the PEMDAS rule to solve the problem 3 × 10 + 8 ÷ 2 - (3 + 5).
Understanding the Problem
The problem given is 3 × 10 + 8 ÷ 2 - (3 + 5). To solve this problem, we need to follow the order of operations, which is:
- Evaluate expressions inside parentheses
- Evaluate any exponential expressions
- Evaluate any multiplication and division operations from left to right
- Evaluate any addition and subtraction operations from left to right
Step 1: Evaluate Expressions Inside Parentheses
The first step in solving the problem is to evaluate the expression inside the parentheses. The expression inside the parentheses is (3 + 5). To evaluate this expression, we need to add 3 and 5.
3 + 5 = 8
So, the expression inside the parentheses is equal to 8.
Step 2: Evaluate Exponential Expressions
There are no exponential expressions in the problem, so we can move on to the next step.
Step 3: Evaluate Multiplication and Division Operations
The next step is to evaluate any multiplication and division operations from left to right. The problem contains two multiplication operations: 3 × 10 and 8 ÷ 2. We need to evaluate these operations first.
3 × 10 = 30
8 ÷ 2 = 4
So, the multiplication and division operations are equal to 30 and 4, respectively.
Step 4: Evaluate Addition and Subtraction Operations
The final step is to evaluate any addition and subtraction operations from left to right. The problem contains two addition and subtraction operations: 30 + 4 and 8 - 30. We need to evaluate these operations last.
30 + 4 = 34
8 - 30 = -22
So, the addition and subtraction operations are equal to 34 and -22, respectively.
Conclusion
To solve the problem 3 × 10 + 8 ÷ 2 - (3 + 5), we need to follow the order of operations, which is:
- Evaluate expressions inside parentheses
- Evaluate any exponential expressions
- Evaluate any multiplication and division operations from left to right
- Evaluate any addition and subtraction operations from left to right
By following these steps, we can evaluate the problem and find the solution.
Final Answer
The final answer to the problem 3 × 10 + 8 ÷ 2 - (3 + 5) is:
-22
This is the solution to the problem.
Importance of Following the Order of Operations
Following the order of operations is crucial in mathematics because it ensures that mathematical expressions are evaluated consistently and accurately. Without following the order of operations, mathematical expressions can be evaluated incorrectly, leading to incorrect solutions.
Real-World Applications of the Order of Operations
The order of operations has many real-world applications, including:
- Computer programming: The order of operations is used in computer programming to evaluate mathematical expressions and ensure that they are evaluated consistently and accurately.
- Science and engineering: The order of operations is used in science and engineering to evaluate mathematical expressions and ensure that they are evaluated consistently and accurately.
- Finance: The order of operations is used in finance to evaluate mathematical expressions and ensure that they are evaluated consistently and accurately.
Conclusion
In conclusion, solving the problem 3 × 10 + 8 ÷ 2 - (3 + 5) requires following the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. By following these steps, we can evaluate the problem and find the solution. The order of operations has many real-world applications, including computer programming, science and engineering, and finance.
Introduction
In our previous article, we solved the problem 3 × 10 + 8 ÷ 2 - (3 + 5) using the order of operations. In this article, we will answer some frequently asked questions about the problem and provide additional information to help you understand the solution.
Q&A
Q: What is the order of operations?
A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is often remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Q: Why is it important to follow the order of operations?
A: Following the order of operations is crucial in mathematics because it ensures that mathematical expressions are evaluated consistently and accurately. Without following the order of operations, mathematical expressions can be evaluated incorrectly, leading to incorrect solutions.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both arithmetic operations that involve numbers. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.
Q: How do I evaluate expressions inside parentheses?
A: To evaluate expressions inside parentheses, you need to follow the order of operations. First, evaluate any exponential expressions, then evaluate any multiplication and division operations from left to right, and finally evaluate any addition and subtraction operations from left to right.
Q: What is the final answer to the problem 3 × 10 + 8 ÷ 2 - (3 + 5)?
A: The final answer to the problem 3 × 10 + 8 ÷ 2 - (3 + 5) is -22.
Q: Can you explain the solution to the problem in more detail?
A: To solve the problem 3 × 10 + 8 ÷ 2 - (3 + 5), we need to follow the order of operations. First, we evaluate the expression inside the parentheses, which is (3 + 5). This expression is equal to 8. Next, we evaluate the multiplication and division operations, which are 3 × 10 and 8 ÷ 2. These operations are equal to 30 and 4, respectively. Finally, we evaluate the addition and subtraction operations, which are 30 + 4 and 8 - 30. These operations are equal to 34 and -22, respectively.
Q: What are some real-world applications of the order of operations?
A: The order of operations has many real-world applications, including computer programming, science and engineering, and finance. In computer programming, the order of operations is used to evaluate mathematical expressions and ensure that they are evaluated consistently and accurately. In science and engineering, the order of operations is used to evaluate mathematical expressions and ensure that they are evaluated consistently and accurately. In finance, the order of operations is used to evaluate mathematical expressions and ensure that they are evaluated consistently and accurately.
Conclusion
In conclusion, solving the problem 3 × 10 + 8 ÷ 2 - (3 + 5) requires following the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. By following these steps, we can evaluate the problem and find the solution. We hope that this Q&A article has provided you with a better understanding of the solution and the importance of following the order of operations.
Additional Resources
- Order of Operations: A set of rules that dictate the order in which mathematical operations should be performed.
- PEMDAS: An acronym that stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
- Computer Programming: The use of computers to solve mathematical problems and perform other tasks.
- Science and Engineering: The use of scientific and engineering principles to solve mathematical problems and perform other tasks.
- Finance: The use of mathematical expressions to evaluate financial transactions and make financial decisions.
Final Answer
The final answer to the problem 3 × 10 + 8 ÷ 2 - (3 + 5) is -22.