Simplify The Expression:${ 63: 7 + (12 - 8) \times (5 \times 2) - 18 + 4 }$
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Introduction
Mathematical expressions can be complex and overwhelming, especially when dealing with multiple operations and parentheses. In this article, we will simplify the given expression: $ 63$. We will break down the expression into manageable parts, apply the order of operations, and finally arrive at the simplified result.
Understanding the Order of Operations
Before we dive into simplifying the expression, it's essential to understand the order of operations. The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:
- 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.
Simplifying the Expression
Now that we have a solid understanding of the order of operations, let's simplify the given expression:
Step 1: Evaluate Expressions Inside Parentheses
The first step is to evaluate the expressions inside the parentheses. We have two sets of parentheses:
Let's evaluate these expressions:
Step 2: Substitute the Evaluated Expressions
Now that we have evaluated the expressions inside the parentheses, we can substitute the results back into the original expression:
Step 3: Multiply the Evaluated Expressions
Next, we need to multiply the evaluated expressions:
Step 4: Add and Subtract from Left to Right
Finally, we can add and subtract the numbers from left to right:
Step 5: Final Result
And there you have it! The final result of the simplified expression is:
Conclusion
Simplifying mathematical expressions can be a daunting task, but by following the order of operations and breaking down the expression into manageable parts, we can arrive at the final result. In this article, we simplified the expression: $ 63$. We hope this guide has been helpful in understanding the order of operations and simplifying mathematical expressions.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I simplify a mathematical expression?
A: To simplify a mathematical expression, follow the order of operations: evaluate expressions inside parentheses, exponents, multiplication and division, and finally addition and subtraction.
Q: What is the final result of the simplified expression?
A: The final result of the simplified expression is 33.
Additional Resources
For more information on simplifying mathematical expressions and the order of operations, check out the following resources:
- Khan Academy: Order of Operations
- Mathway: Simplifying Expressions
- Wolfram Alpha: Order of Operations
By following the steps outlined in this article and practicing with different mathematical expressions, you will become proficient in simplifying expressions and solving mathematical problems with ease.
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Introduction
In our previous article, we simplified the expression: $ 63$. We broke down the expression into manageable parts, applied the order of operations, and finally arrived at the simplified result. In this article, we will answer some frequently asked questions about simplifying mathematical expressions and the order of operations.
Q&A: Simplifying Mathematical Expressions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I simplify a mathematical expression?
A: To simplify a mathematical expression, follow the order of operations: evaluate expressions inside parentheses, exponents, multiplication and division, and finally addition and subtraction.
Q: What is the difference between PEMDAS and BODMAS?
A: PEMDAS and BODMAS are both acronyms used to remember the order of operations. PEMDAS is commonly used in the United States, while BODMAS is commonly used in the United Kingdom and other countries. The order of operations is the same for both acronyms.
Q: How do I handle negative numbers in mathematical expressions?
A: When working with negative numbers, remember that multiplication and division operations are performed before addition and subtraction operations. For example, in the expression , the multiplication operation is performed first, resulting in .
Q: Can I simplify an expression with multiple parentheses?
A: Yes, you can simplify an expression with multiple parentheses by following the order of operations. Evaluate the expressions inside the innermost parentheses first, and then work your way outwards.
Q: How do I handle fractions in mathematical expressions?
A: When working with fractions, remember to simplify the fraction before performing any operations. For example, in the expression , the fractions can be simplified by finding a common denominator, resulting in .
Q&A: Common Mistakes in Simplifying Mathematical Expressions
Q: What is the most common mistake when simplifying mathematical expressions?
A: The most common mistake is not following the order of operations. This can lead to incorrect results and confusion.
Q: How can I avoid making mistakes when simplifying mathematical expressions?
A: To avoid making mistakes, take your time and carefully evaluate each operation. Use a calculator or a computer program to check your work, and make sure to follow the order of operations.
Q: What is the difference between a mathematical expression and a mathematical equation?
A: A mathematical expression is a statement that contains variables and constants, while a mathematical equation is a statement that contains an equal sign (=). For example, is a mathematical expression, while is a mathematical equation.
Conclusion
Simplifying mathematical expressions can be a daunting task, but by following the order of operations and breaking down the expression into manageable parts, we can arrive at the final result. In this article, we answered some frequently asked questions about simplifying mathematical expressions and the order of operations. We hope this guide has been helpful in understanding the order of operations and simplifying mathematical expressions.
Frequently Asked Questions
Q: What is the order of operations?
A: The order of operations is a set of rules that dictates the order in which mathematical operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I simplify a mathematical expression?
A: To simplify a mathematical expression, follow the order of operations: evaluate expressions inside parentheses, exponents, multiplication and division, and finally addition and subtraction.
Q: What is the final result of the simplified expression?
A: The final result of the simplified expression is 33.
Additional Resources
For more information on simplifying mathematical expressions and the order of operations, check out the following resources:
- Khan Academy: Order of Operations
- Mathway: Simplifying Expressions
- Wolfram Alpha: Order of Operations
By following the steps outlined in this article and practicing with different mathematical expressions, you will become proficient in simplifying expressions and solving mathematical problems with ease.