Find The Value Of Each Expression:$15 \div 5 \times 3 + 8 - 3$a. 6 B. 30 C. 14 D. 17 Please Select The Best Answer From The Choices Provided:A, B, C, D
Introduction
Mathematical expressions are a fundamental part of mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific type of mathematical expression, which involves a combination of arithmetic operations such as division, multiplication, addition, and subtraction. We will use the expression $15 \div 5 \times 3 + 8 - 3$ as an example and walk through the steps to find its value.
Understanding the Order of Operations
Before we dive into solving the expression, it's essential to understand 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: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Solving the Expression
Now that we have a good understanding of the order of operations, let's apply it to the given expression:
Step 1: Division
The first operation to perform is the division. According to the order of operations, we need to evaluate the expression inside the parentheses first. In this case, there are no parentheses, so we move on to the next operation, which is the division.
Step 2: Multiplication
Next, we need to perform the multiplication operation. According to the order of operations, we need to evaluate the multiplication operation from left to right.
Step 3: Addition and Subtraction
Now that we have the result of the multiplication operation, we can move on to the addition and subtraction operations. According to the order of operations, we need to evaluate the addition and subtraction operations from left to right.
Step 4: Final Result
Finally, we need to subtract 3 from the result of the addition operation.
Conclusion
In conclusion, the value of the expression $15 \div 5 \times 3 + 8 - 3$ is 14. This is the correct answer, and it can be verified by following the order of operations and performing the arithmetic operations in the correct order.
Answer
The correct answer is:
- C. 14
Why is this the correct answer?
This is the correct answer because it follows the order of operations and performs the arithmetic operations in the correct order. The expression is evaluated as follows:
- Division: 15 ÷ 5 = 3
- Multiplication: 3 × 3 = 9
- Addition: 9 + 8 = 17
- Subtraction: 17 - 3 = 14
Therefore, the value of the expression is 14.
Tips and Tricks
Here are some tips and tricks to help you solve mathematical expressions like this one:
- Always follow the order of operations.
- Evaluate expressions inside parentheses first.
- Evaluate any exponential expressions next.
- Evaluate multiplication and division operations from left to right.
- Finally, evaluate any addition and subtraction operations from left to right.
By following these tips and tricks, you can solve mathematical expressions like this one with ease.
Common Mistakes
Here are some common mistakes to avoid when solving mathematical expressions like this one:
- Not following the order of operations.
- Evaluating expressions in the wrong order.
- Not evaluating expressions inside parentheses first.
- Not evaluating any exponential expressions.
By avoiding these common mistakes, you can ensure that you get the correct answer.
Real-World Applications
Mathematical expressions like this one have many real-world applications. For example, they can be used to solve problems in finance, engineering, and science. They can also be used to model real-world situations and make predictions about future events.
Conclusion
Introduction
In our previous article, we discussed how to solve mathematical expressions using the order of operations. We walked through a step-by-step example of how to evaluate the expression $15 \div 5 \times 3 + 8 - 3$. In this article, we will provide a Q&A guide to help you better understand how to solve mathematical expressions.
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: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: Why is it important to follow the order of operations?
A: Following the order of operations is crucial to ensure that mathematical expressions are evaluated correctly. If the order of operations is not followed, the result of the expression may be incorrect.
Q: What happens if there are no parentheses in an expression?
A: If there are no parentheses in an expression, the next operation to perform is the exponentiation operation. If there are no exponents in the expression, the next operation to perform is the multiplication and division operation.
Q: What is the difference between multiplication and division?
A: Multiplication and division are both arithmetic operations that involve numbers. However, the key difference between the two is that multiplication involves repeated addition, while division involves repeated subtraction.
Q: How do I evaluate an expression with multiple operations?
A: To evaluate an expression with multiple operations, follow the order of operations. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.
Q: What are some common mistakes to avoid when solving mathematical expressions?
A: Some common mistakes to avoid when solving mathematical expressions include:
- Not following the order of operations.
- Evaluating expressions in the wrong order.
- Not evaluating expressions inside parentheses first.
- Not evaluating any exponential expressions.
Q: How can I practice solving mathematical expressions?
A: There are many ways to practice solving mathematical expressions, including:
- Working through practice problems in a textbook or online resource.
- Using online tools or apps to generate random mathematical expressions.
- Creating your own mathematical expressions to solve.
Q: What are some real-world applications of mathematical expressions?
A: Mathematical expressions have many real-world applications, including:
- Solving problems in finance, engineering, and science.
- Modeling real-world situations and making predictions about future events.
- Creating algorithms and computer programs.
Conclusion
In conclusion, solving mathematical expressions requires a good understanding of the order of operations and the ability to perform arithmetic operations in the correct order. By following the tips and tricks outlined in this article, you can improve your skills and become proficient in solving mathematical expressions. Remember to always follow the order of operations and evaluate expressions inside parentheses first. With practice and patience, you can become proficient in solving mathematical expressions like a pro!
Additional Resources
For more information on solving mathematical expressions, check out the following resources:
- Khan Academy: Mathematical Expressions
- Mathway: Mathematical Expression Solver
- Wolfram Alpha: Mathematical Expression Solver
Final Tips
- Always follow the order of operations.
- Evaluate expressions inside parentheses first.
- Evaluate any exponential expressions next.
- Evaluate multiplication and division operations from left to right.
- Finally, evaluate any addition and subtraction operations from left to right.
By following these tips and practicing regularly, you can become proficient in solving mathematical expressions and tackle even the most challenging problems with confidence!