Evaluate The Expression: $ 7 \times (10 - 10) $
Introduction
In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves simplifying it to a single value. In this article, we will evaluate the expression $ 7 \times (10 - 10) $, which involves the use of parentheses, multiplication, and subtraction.
Understanding the Order of Operations
To evaluate the expression $ 7 \times (10 - 10) $, we need to follow 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 any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Evaluating the Expression Inside the Parentheses
The expression inside the parentheses is $ 10 - 10 $. To evaluate this expression, we need to subtract 10 from 10.
$ 10 - 10 = 0 $
Evaluating the Expression Outside the Parentheses
Now that we have evaluated the expression inside the parentheses, we can evaluate the expression outside the parentheses. The expression outside the parentheses is $ 7 \times 0 $.
$ 7 \times 0 = 0 $
Conclusion
In conclusion, the expression $ 7 \times (10 - 10) $ evaluates to 0. This is because the expression inside the parentheses evaluates to 0, and any number multiplied by 0 is equal to 0.
Real-World Applications
Evaluating expressions like $ 7 \times (10 - 10) $ may seem like a trivial task, but it has real-world applications in various fields such as science, engineering, and finance. For example, in physics, the expression $ 7 \times (10 - 10) $ may be used to calculate the energy of a system, while in finance, it may be used to calculate the value of an investment.
Tips and Tricks
When evaluating expressions, it's essential to follow the order of operations and to simplify the expression step by step. Here are some tips and tricks to help you evaluate expressions like $ 7 \times (10 - 10) $:
- Use parentheses: Parentheses can help to clarify the order of operations and prevent errors.
- Simplify expressions: Simplify expressions step by step to avoid confusion.
- Use the order of operations: Follow the order of operations (PEMDAS) to ensure that you evaluate expressions correctly.
Common Mistakes
When evaluating expressions like $ 7 \times (10 - 10) $, there are several common mistakes that you should avoid:
- Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
- Not simplifying expressions: Failing to simplify expressions can lead to confusion and errors.
- Not using parentheses: Failing to use parentheses can lead to ambiguity and errors.
Final Thoughts
Evaluating expressions like $ 7 \times (10 - 10) $ may seem like a simple task, but it requires attention to detail and a clear understanding of the order of operations. By following the order of operations and simplifying expressions step by step, you can ensure that you evaluate expressions correctly and avoid common mistakes.
Frequently Asked Questions
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 any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate expressions with parentheses?
A: To evaluate expressions with parentheses, you need to follow the order of operations. First, evaluate the expression inside the parentheses, and then evaluate the expression outside the parentheses.
Q: What is the result of the expression $ 7 \times (10 - 10) $?
A: The result of the expression $ 7 \times (10 - 10) $ is 0. This is because the expression inside the parentheses evaluates to 0, and any number multiplied by 0 is equal to 0.
Introduction
Evaluating expressions with parentheses can be a challenging task, but with the right approach, it can be done with ease. In this article, we will answer some frequently asked questions about evaluating expressions with parentheses.
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: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate expressions with parentheses?
A: To evaluate expressions with parentheses, you need to follow the order of operations. First, evaluate the expression inside the parentheses, and then evaluate the expression outside the parentheses.
Q: What is the result of the expression $ 7 \times (10 - 10) $?
A: The result of the expression $ 7 \times (10 - 10) $ is 0. This is because the expression inside the parentheses evaluates to 0, and any number multiplied by 0 is equal to 0.
Q: What is the result of the expression $ (5 + 3) \times 2 $?
A: The result of the expression $ (5 + 3) \times 2 $ is 16. First, evaluate the expression inside the parentheses, which is $ 5 + 3 = 8 $. Then, multiply 8 by 2, which is $ 8 \times 2 = 16 $.
Q: What is the result of the expression $ 10 - (5 + 3) $?
A: The result of the expression $ 10 - (5 + 3) $ is 2. First, evaluate the expression inside the parentheses, which is $ 5 + 3 = 8 $. Then, subtract 8 from 10, which is $ 10 - 8 = 2 $.
Q: What is the result of the expression $ (10 - 5) \times (3 + 2) $?
A: The result of the expression $ (10 - 5) \times (3 + 2) $ is 15. First, evaluate the expression inside the parentheses, which is $ 10 - 5 = 5 $ and $ 3 + 2 = 5 $. Then, multiply 5 by 5, which is $ 5 \times 5 = 25 $.
Q: What is the result of the expression $ (10 - 5) \times (3 + 2) $ if the order of operations is not followed?
A: If the order of operations is not followed, the result of the expression $ (10 - 5) \times (3 + 2) $ will be incorrect. In this case, the expression inside the parentheses will be evaluated as $ 10 - 5 = 5 $ and $ 3 + 2 = 5 $, but then the multiplication will be performed as $ 5 \times 3 = 15 $ and $ 5 \times 2 = 10 $, resulting in an incorrect answer of 150.
Conclusion
Evaluating expressions with parentheses requires attention to detail and a clear understanding of the order of operations. By following the order of operations and simplifying expressions step by step, you can ensure that you evaluate expressions correctly and avoid common mistakes.
Tips and Tricks
- Use parentheses: Parentheses can help to clarify the order of operations and prevent errors.
- Simplify expressions: Simplify expressions step by step to avoid confusion.
- Use the order of operations: Follow the order of operations (PEMDAS) to ensure that you evaluate expressions correctly.
Common Mistakes
- Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
- Not simplifying expressions: Failing to simplify expressions can lead to confusion and errors.
- Not using parentheses: Failing to use parentheses can lead to ambiguity and errors.
Final Thoughts
Evaluating expressions with parentheses is a crucial skill in mathematics, and with practice and patience, you can master it. Remember to follow the order of operations, simplify expressions step by step, and use parentheses to clarify the order of operations.