Evaluate The Expression: ${ 10 + \frac{280}{12} }$
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Introduction
In mathematics, evaluating expressions is a fundamental concept that involves simplifying mathematical statements to obtain a numerical value. In this article, we will focus on evaluating the expression 10 + 280/12, which involves addition and division operations. We will break down the expression into smaller steps, apply the order of operations, and simplify the result to obtain the final answer.
Understanding the Order of Operations
The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression. 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.
Breaking Down the Expression
The given expression is 10 + 280/12. To evaluate this expression, we need to follow the order of operations. First, we need to evaluate the division operation 280/12.
Evaluating the Division Operation
To evaluate the division operation 280/12, we can use long division or a calculator. Using long division, we can divide 280 by 12 as follows:
280 ÷ 12 = 23.33
Alternatively, we can use a calculator to evaluate the division operation:
280 ÷ 12 = 23.3333
Evaluating the Addition Operation
Now that we have evaluated the division operation, we can evaluate the addition operation 10 + 280/12. We can substitute the result of the division operation into the expression:
10 + 280/12 = 10 + 23.33
Simplifying the Result
To simplify the result, we can add 10 and 23.33:
10 + 23.33 = 33.33
Conclusion
In this article, we evaluated the expression 10 + 280/12 by following the order of operations. We first evaluated the division operation 280/12, and then evaluated the addition operation 10 + 280/12. Finally, we simplified the result to obtain the final answer, which is 33.33.
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 when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I evaluate the expression 10 + 280/12?
A: To evaluate the expression 10 + 280/12, you need to follow the order of operations. First, evaluate the division operation 280/12, and then evaluate the addition operation 10 + 280/12.
Q: What is the final answer to the expression 10 + 280/12?
A: The final answer to the expression 10 + 280/12 is 33.33.
Additional Resources
For more information on evaluating expressions and the order of operations, you can refer to the following resources:
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
Related Articles
- Evaluating Expressions with Exponents
- Evaluating Expressions with Fractions
- Order of Operations: A Guide to Evaluating Mathematical Expressions
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Introduction
In our previous article, we evaluated the expression 10 + 280/12 by following the order of operations. In this article, we will answer some frequently asked questions related to evaluating expressions and the order of operations.
Q&A
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 when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I evaluate the expression 10 + 280/12?
A: To evaluate the expression 10 + 280/12, you need to follow the order of operations. First, evaluate the division operation 280/12, and then evaluate the addition operation 10 + 280/12.
Q: What is the final answer to the expression 10 + 280/12?
A: The final answer to the expression 10 + 280/12 is 33.33.
Q: What is the difference between PEMDAS and BODMAS?
A: PEMDAS and BODMAS are two different notations 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. Both notations follow the same 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.
Q: How do I evaluate an expression with multiple operations?
A: To evaluate an expression with multiple operations, you need to follow the order of operations. First, evaluate any expressions inside parentheses, then evaluate any exponential expressions, followed by multiplication and division operations from left to right, and finally evaluate any addition and subtraction operations from left to right.
Q: What is the importance of following 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 results.
Q: Can I use a calculator to evaluate mathematical expressions?
A: Yes, you can use a calculator to evaluate mathematical expressions. However, it's essential to understand the order of operations and how to evaluate expressions manually to ensure that you understand the underlying mathematics.
Conclusion
In this article, we answered some frequently asked questions related to evaluating expressions and the order of operations. We hope that this article has provided you with a better understanding of the importance of following the order of operations and how to evaluate 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 when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I evaluate the expression 10 + 280/12?
A: To evaluate the expression 10 + 280/12, you need to follow the order of operations. First, evaluate the division operation 280/12, and then evaluate the addition operation 10 + 280/12.
Q: What is the final answer to the expression 10 + 280/12?
A: The final answer to the expression 10 + 280/12 is 33.33.
Additional Resources
For more information on evaluating expressions and the order of operations, you can refer to the following resources:
- Khan Academy: Order of Operations
- Mathway: Order of Operations
- Wolfram Alpha: Order of Operations
Related Articles
- Evaluating Expressions with Exponents
- Evaluating Expressions with Fractions
- Order of Operations: A Guide to Evaluating Mathematical Expressions