Which Is NOT Equivalent To $3(4+5)$?A. $3(4)+3(5)$ B. $ 3 ( 5 + 4 ) 3(5+4) 3 ( 5 + 4 ) [/tex] C. $12+15$ D. $3(4)+5$
Introduction
When it comes to mathematical expressions, equivalence is a crucial concept. Two expressions are said to be equivalent if they have the same value. In this article, we will explore the concept of equivalence in mathematical expressions, focusing on the given expression $3(4+5)$. We will examine four different expressions and determine which one is NOT equivalent to the given expression.
Understanding the Given Expression
The given expression is $3(4+5)$. To evaluate this expression, we need to follow the order of operations (PEMDAS):
- Evaluate the expression inside the parentheses: $4+5 = 9$
- Multiply 3 by the result: $3 \times 9 = 27$
Therefore, the value of the given expression is 27.
Expression A: $3(4)+3(5)$
Let's evaluate Expression A:
- Evaluate the expression inside the parentheses: $4+5 = 9$
- Multiply 3 by 4: $3 \times 4 = 12$
- Multiply 3 by 5: $3 \times 5 = 15$
- Add the results: $12 + 15 = 27$
Expression A is equivalent to the given expression.
Expression B: $3(5+4)$
Let's evaluate Expression B:
- Evaluate the expression inside the parentheses: $5+4 = 9$
- Multiply 3 by the result: $3 \times 9 = 27$
Expression B is equivalent to the given expression.
Expression C: $12+15$
Let's evaluate Expression C:
- Add the numbers: $12 + 15 = 27$
Expression C is equivalent to the given expression.
Expression D: $3(4)+5$
Let's evaluate Expression D:
- Multiply 3 by 4: $3 \times 4 = 12$
- Add 5 to the result: $12 + 5 = 17$
Expression D is NOT equivalent to the given expression.
Conclusion
In conclusion, the expression that is NOT equivalent to $3(4+5)$ is Expression D: $3(4)+5$. This is because the order of operations is not followed correctly in Expression D, resulting in a different value.
Importance of Equivalence in Mathematics
Equivalence is a fundamental concept in mathematics, and it plays a crucial role in various mathematical operations. Understanding equivalence helps students to:
- Simplify complex expressions
- Evaluate mathematical expressions accurately
- Identify equivalent expressions
- Solve mathematical problems efficiently
Tips for Evaluating Mathematical Expressions
When evaluating mathematical expressions, follow these tips:
- Follow the order of operations (PEMDAS)
- Evaluate expressions inside parentheses first
- Multiply and divide numbers from left to right
- Add and subtract numbers from left to right
- Check for equivalent expressions
Common Mistakes in Evaluating Mathematical Expressions
Some common mistakes to avoid when evaluating mathematical expressions include:
- Not following the order of operations
- Evaluating expressions incorrectly
- Not checking for equivalent expressions
- Not simplifying complex expressions
Final Thoughts
In conclusion, equivalence is a crucial concept in mathematics, and it plays a vital role in evaluating mathematical expressions. By understanding equivalence and following the tips provided, students can simplify complex expressions, evaluate mathematical expressions accurately, and identify equivalent expressions. Remember, practice makes perfect, so make sure to practice evaluating mathematical expressions regularly to become proficient in this skill.
Introduction
In our previous article, we explored the concept of equivalence in mathematics, focusing on the expression $3(4+5)$. We examined four different expressions and determined which one is NOT equivalent to the given expression. In this article, we will address some frequently asked questions (FAQs) on equivalence in mathematics.
Q: What is equivalence in mathematics?
A: Equivalence in mathematics refers to the relationship between two or more mathematical expressions that have the same value. In other words, two expressions are equivalent if they can be simplified to the same result.
Q: How do I determine if two expressions are equivalent?
A: To determine if two expressions are equivalent, follow these steps:
- Simplify both expressions using the order of operations (PEMDAS)
- Evaluate both expressions
- Compare the results
If the results are the same, then the expressions are equivalent.
Q: What are some common examples of equivalent expressions?
A: Some common examples of equivalent expressions include:
-
2(3+4)$ and $2(7)
-
5(2+3)$ and $5(5)
-
3(4+5)$ and $3(9)
Q: What are some common mistakes to avoid when evaluating equivalent expressions?
A: Some common mistakes to avoid when evaluating equivalent expressions include:
- Not following the order of operations
- Evaluating expressions incorrectly
- Not checking for equivalent expressions
- Not simplifying complex expressions
Q: How can I practice evaluating equivalent expressions?
A: To practice evaluating equivalent expressions, try the following:
- Simplify complex expressions using the order of operations (PEMDAS)
- Evaluate expressions using different methods (e.g., using a calculator or by hand)
- Compare the results of different expressions to determine if they are equivalent
- Practice solving mathematical problems that involve equivalent expressions
Q: What are some real-world applications of equivalence in mathematics?
A: Equivalence in mathematics has many real-world applications, including:
- Simplifying complex financial calculations
- Evaluating the cost of different products or services
- Determining the value of different investments
- Solving problems in physics, engineering, and other fields that involve mathematical modeling
Q: Can I use technology to evaluate equivalent expressions?
A: Yes, you can use technology to evaluate equivalent expressions. Many calculators and computer software programs can simplify complex expressions and evaluate them quickly and accurately.
Q: How can I use equivalence in mathematics to solve problems?
A: To use equivalence in mathematics to solve problems, follow these steps:
- Identify the problem and the mathematical expression involved
- Simplify the expression using the order of operations (PEMDAS)
- Evaluate the expression
- Compare the results to determine if the expression is equivalent to the original problem
By following these steps, you can use equivalence in mathematics to solve a wide range of problems.
Conclusion
In conclusion, equivalence in mathematics is a fundamental concept that plays a crucial role in evaluating mathematical expressions. By understanding equivalence and following the tips provided, you can simplify complex expressions, evaluate mathematical expressions accurately, and identify equivalent expressions. Remember, practice makes perfect, so make sure to practice evaluating mathematical expressions regularly to become proficient in this skill.