Evaluate The Expression: $25 + (65 - 5) \times 20 \div 2^2$
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Introduction
In mathematics, expressions are a fundamental concept that helps us represent and solve problems. Evaluating an expression involves simplifying it to a single value, which can be a number, a variable, or even an algebraic expression. In this article, we will focus on evaluating a complex expression that involves various mathematical operations, including addition, subtraction, multiplication, and division.
The Expression
The expression we will be evaluating is:
This expression involves several operations, including parentheses, exponents, multiplication, and division. To evaluate this expression, we need to follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
Step 1: Evaluate the Expression Inside the Parentheses
The first step is to evaluate the expression inside the parentheses:
To do this, we need to subtract 5 from 65:
Step 2: Evaluate the Exponent
Next, we need to evaluate the exponent:
To do this, we need to raise 2 to the power of 2:
Step 3: Multiply 60 by 20
Now, we need to multiply 60 by 20:
Step 4: Divide 1200 by 4
Next, we need to divide 1200 by 4:
Step 5: Add 25 to 300
Finally, we need to add 25 to 300:
Conclusion
In conclusion, the final value of the expression is 325. To evaluate this expression, we need to follow the order of operations (PEMDAS) and simplify the expression step by step. By breaking down the expression into smaller parts and evaluating each part separately, we can arrive at the final value.
Tips and Tricks
When evaluating complex expressions, it's essential to follow the order of operations (PEMDAS) and simplify the expression step by step. Here are some tips and tricks to help you evaluate expressions like this:
- Use parentheses: Parentheses help to group numbers and operations together, making it easier to evaluate the expression.
- Evaluate exponents first: Exponents should be evaluated before any other operations.
- Multiply and divide from left to right: When there are multiple multiplication and division operations, they should be evaluated from left to right.
- Add and subtract from left to right: When there are multiple addition and subtraction operations, they should be evaluated from left to right.
Real-World Applications
Evaluating expressions like this has many real-world applications. For example:
- Science and engineering: In science and engineering, expressions are used to model real-world problems and make predictions.
- Finance: In finance, expressions are used to calculate interest rates, investments, and other financial metrics.
- Computer programming: In computer programming, expressions are used to write algorithms and solve problems.
Final Thoughts
In conclusion, evaluating expressions like this requires a deep understanding of mathematical operations and the order of operations (PEMDAS). By following these steps and using the tips and tricks outlined above, you can simplify complex expressions and arrive at the final value. Whether you're a student, a professional, or simply someone who loves math, understanding how to evaluate expressions is an essential skill that can help you solve problems and make predictions in many areas of life.
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Introduction
In our previous article, we explored how to evaluate a complex expression using the order of operations (PEMDAS). However, we know that math can be a challenging subject, and sometimes it's helpful to have a Q&A guide to clarify any doubts or questions you may have. In this article, we'll answer some frequently asked questions about evaluating expressions, covering topics such as the order of operations, parentheses, and exponents.
Q&A
Q: What is the order of operations (PEMDAS)?
A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next (e.g., 2^3).
- 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: Why do we need to follow the order of operations?
A: Following the order of operations ensures that we evaluate expressions in a consistent and predictable way. This helps to avoid confusion and ensures that we get the correct answer.
Q: What happens if there are multiple operations with the same precedence?
A: If there are multiple operations with the same precedence (e.g., two multiplication operations), we evaluate them from left to right. For example, in the expression 3 × 4 × 5, we would first multiply 3 and 4, then multiply the result by 5.
Q: How do we handle parentheses with multiple operations inside?
A: When there are multiple operations inside parentheses, we evaluate them from left to right, following the order of operations. For example, in the expression (2 + 3) × 4, we would first evaluate the expression inside the parentheses (2 + 3), then multiply the result by 4.
Q: What is the difference between an exponent and a power?
A: An exponent and a power are often used interchangeably, but technically, an exponent is a small number that is raised to a power, while a power is the result of raising a number to a certain exponent. For example, in the expression 2^3, the 3 is an exponent, and the result is a power (8).
Q: Can you give an example of an expression with multiple operations and parentheses?
A: Here's an example:
(2 + 3) × (4 - 2) + 5
To evaluate this expression, we would follow the order of operations:
- Evaluate the expressions inside the parentheses: (2 + 3) = 5 and (4 - 2) = 2.
- Multiply the results: 5 × 2 = 10.
- Add 5 to the result: 10 + 5 = 15.
Q: What if I get stuck or make a mistake while evaluating an expression?
A: Don't worry! If you get stuck or make a mistake, try breaking down the expression into smaller parts and evaluating each part separately. You can also use a calculator or ask a friend or teacher for help.
Conclusion
Evaluating expressions can be a challenging task, but with practice and patience, you can become proficient in following the order of operations and simplifying complex expressions. Remember to always follow the order of operations (PEMDAS) and use parentheses to group numbers and operations together. If you have any more questions or need further clarification, feel free to ask!
Tips and Tricks
- Use a calculator: If you're struggling to evaluate an expression, try using a calculator to check your work.
- Break down the expression: Break down the expression into smaller parts and evaluate each part separately.
- Use parentheses: Use parentheses to group numbers and operations together, making it easier to evaluate the expression.
- Check your work: Double-check your work to ensure that you've followed the order of operations correctly.
Real-World Applications
Evaluating expressions has many real-world applications, including:
- Science and engineering: In science and engineering, expressions are used to model real-world problems and make predictions.
- Finance: In finance, expressions are used to calculate interest rates, investments, and other financial metrics.
- Computer programming: In computer programming, expressions are used to write algorithms and solve problems.
Final Thoughts
In conclusion, evaluating expressions is an essential skill that requires practice and patience. By following the order of operations (PEMDAS) and using parentheses to group numbers and operations together, you can simplify complex expressions and arrive at the final value. Whether you're a student, a professional, or simply someone who loves math, understanding how to evaluate expressions is an essential skill that can help you solve problems and make predictions in many areas of life.