Calculate The Expression:${ 40 - 65 \div 13 + 14 \times 15 }$
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Introduction
In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves performing the operations in the correct order to obtain a result. In this article, we will focus on calculating the expression: 40 - 65 ÷ 13 + 14 × 15. We will break down the expression into smaller parts, apply the order of operations, and finally obtain the result.
Order of Operations
The order of operations is a set of rules that dictate 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.
Breaking Down the Expression
Let's break down the expression: 40 - 65 ÷ 13 + 14 × 15.
Step 1: Evaluate the Division Operation
The expression contains a division operation: 65 ÷ 13. According to the order of operations, we should evaluate this operation first.
65 ÷ 13 = 5
So, the expression becomes: 40 - 5 + 14 × 15.
Step 2: Evaluate the Multiplication Operation
The expression contains a multiplication operation: 14 × 15. According to the order of operations, we should evaluate this operation next.
14 × 15 = 210
So, the expression becomes: 40 - 5 + 210.
Step 3: Evaluate the Addition and Subtraction Operations
Now that we have evaluated the division and multiplication operations, we can evaluate the addition and subtraction operations from left to right.
First, we subtract 5 from 40:
40 - 5 = 35
Then, we add 210 to 35:
35 + 210 = 245
Conclusion
In this article, we calculated the expression: 40 - 65 ÷ 13 + 14 × 15. We broke down the expression into smaller parts, applied the order of operations, and finally obtained the result: 245.
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 acronym PEMDAS is commonly used to remember the order of operations.
Q: How do I evaluate an expression with multiple operations?
A: To evaluate an expression with multiple operations, follow the order of operations: parentheses, exponents, multiplication and division, and finally addition and subtraction.
Q: What is the result of the expression: 40 - 65 ÷ 13 + 14 × 15?
A: The result of the expression: 40 - 65 ÷ 13 + 14 × 15 is 245.
Final Thoughts
Calculating expressions is an essential skill in mathematics. By following the order of operations and breaking down complex expressions into smaller parts, we can evaluate even the most challenging expressions. In this article, we calculated the expression: 40 - 65 ÷ 13 + 14 × 15 and obtained the result: 245. We hope this article has provided you with a better understanding of how to calculate expressions and has helped you to improve your math skills.
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Introduction
Calculating expressions is a fundamental concept in mathematics. In our previous article, we discussed how to calculate the expression: 40 - 65 ÷ 13 + 14 × 15. In this article, we will answer some frequently asked questions related to calculating expressions.
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 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.
Q: How do I evaluate an expression with multiple operations?
A: To evaluate an expression with multiple operations, follow the order of operations:
- Identify the operations in the expression.
- Evaluate the operations in the correct order (PEMDAS).
- Simplify the expression by combining like terms.
Q: What is the difference between addition and subtraction?
A: Addition and subtraction are both binary operations that combine two numbers. The difference between addition and subtraction is the direction of the operation:
- Addition: Combine two numbers by adding them together.
- Subtraction: Combine two numbers by subtracting one number from another.
Q: How do I evaluate an expression with parentheses?
A: To evaluate an expression with parentheses, follow these steps:
- Evaluate the expression inside the parentheses first.
- Simplify the expression by combining like terms.
- Evaluate the remaining operations in the correct order (PEMDAS).
Q: What is the result of the expression: 40 - 65 ÷ 13 + 14 × 15?
A: The result of the expression: 40 - 65 ÷ 13 + 14 × 15 is 245.
Q: How do I simplify an expression with multiple operations?
A: To simplify an expression with multiple operations, follow these steps:
- Identify the operations in the expression.
- Evaluate the operations in the correct order (PEMDAS).
- Combine like terms to simplify the expression.
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 expressions are evaluated correctly. If the order of operations is not followed, the result of the expression may be incorrect.
Conclusion
Calculating expressions is a fundamental concept in mathematics. By following the order of operations and breaking down complex expressions into smaller parts, we can evaluate even the most challenging expressions. In this article, we answered some frequently asked questions related to calculating expressions and provided tips and tricks for simplifying expressions.
Final Thoughts
Calculating expressions is an essential skill in mathematics. By practicing and mastering the order of operations, you can become proficient in evaluating complex expressions and solving mathematical problems. Remember to always follow the order of operations and simplify expressions by combining like terms.