Which Expression Matches The Description Shown?16 Plus The Product Of 7 And 8A. $(16 \times 7) + 8$ B. $(16 + 7) \times 8$ C. $16 + (7 \times 8$\] D. $16 \times (7 + 8$\]

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Understanding the Order of Operations

When it comes to mathematical expressions, the order of operations is crucial in determining the correct solution. The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

The Given Expression

The given expression is: 16 plus the product of 7 and 8A.

Breaking Down the Expression

To determine which expression matches the given description, let's break down the expression into smaller parts:

  1. The product of 7 and 8A: This means we need to multiply 7 and 8A.
  2. Adding 16 to the product: This means we need to add 16 to the result of the product.

Evaluating the Options

Now, let's evaluate each option to see which one matches the given description:

Option A: (16×7)+8(16 \times 7) + 8

This option is incorrect because it multiplies 16 and 7, and then adds 8, which is not the product of 7 and 8A.

Option B: (16+7)×8(16 + 7) \times 8

This option is incorrect because it adds 16 and 7, and then multiplies the result by 8, which is not the product of 7 and 8A.

Option C: 16+(7×8)16 + (7 \times 8)

This option is incorrect because it multiplies 7 and 8, and then adds 16, which is not the product of 7 and 8A.

Option D: 16×(7+8)16 \times (7 + 8)

This option is incorrect because it adds 7 and 8, and then multiplies the result by 16, which is not the product of 7 and 8A.

The Correct Answer

However, none of the options match the given description. The correct expression would be:

16+(7×8A)16 + (7 \times 8A)

This expression matches the given description because it adds 16 to the product of 7 and 8A.

Conclusion

In conclusion, the order of operations is crucial in determining the correct solution to a mathematical expression. By following the order of operations, we can evaluate expressions and determine the correct solution. In this case, the correct expression is 16+(7×8A)16 + (7 \times 8A), which matches the given description.

Understanding the Importance of Order of Operations

The order of operations is not just a set of rules, but it's also a way of thinking about mathematical expressions. By following the order of operations, we can ensure that we're evaluating expressions correctly and avoiding errors.

Real-World Applications

The order of operations has many real-world applications, such as:

  • Science and Engineering: The order of operations is used to evaluate complex mathematical expressions in scientific and engineering applications.
  • Finance: The order of operations is used to evaluate financial expressions, such as investment returns and interest rates.
  • Computer Programming: The order of operations is used to evaluate expressions in computer programming languages.

Tips for Evaluating Expressions

Here are some tips for evaluating expressions:

  • Read the expression carefully: Before evaluating an expression, read it carefully to understand what it's asking for.
  • Follow the order of operations: Follow the order of operations to ensure that you're evaluating the expression correctly.
  • Use parentheses: Use parentheses to group expressions and ensure that they're evaluated correctly.
  • Check your work: Check your work to ensure that you've evaluated the expression correctly.

Conclusion

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is the order of operations important?

A: The order of operations is important because it helps us evaluate expressions correctly and avoid errors. Without the order of operations, we might evaluate expressions in the wrong order, leading to incorrect results.

Q: How do I use the order of operations to evaluate expressions?

A: To use the order of operations to evaluate expressions, follow these steps:

  1. Read the expression carefully: Before evaluating an expression, read it carefully to understand what it's asking for.
  2. Follow the order of operations: Follow the order of operations to ensure that you're evaluating the expression correctly.
  3. Use parentheses: Use parentheses to group expressions and ensure that they're evaluated correctly.
  4. Check your work: Check your work to ensure that you've evaluated the expression correctly.

Q: What are some common mistakes to avoid when using the order of operations?

A: Some common mistakes to avoid when using the order of operations include:

  • Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
  • Not using parentheses: Failing to use parentheses can lead to incorrect results.
  • Not checking your work: Failing to check your work can lead to incorrect results.

Q: How do I apply the order of operations to real-world problems?

A: To apply the order of operations to real-world problems, follow these steps:

  1. Read the problem carefully: Before solving a problem, read it carefully to understand what it's asking for.
  2. Identify the operations: Identify the operations involved in the problem, such as addition, subtraction, multiplication, and division.
  3. Apply the order of operations: Apply the order of operations to evaluate the expression correctly.
  4. Check your work: Check your work to ensure that you've solved the problem correctly.

Q: What are some examples of real-world applications of the order of operations?

A: Some examples of real-world applications of the order of operations include:

  • Science and Engineering: The order of operations is used to evaluate complex mathematical expressions in scientific and engineering applications.
  • Finance: The order of operations is used to evaluate financial expressions, such as investment returns and interest rates.
  • Computer Programming: The order of operations is used to evaluate expressions in computer programming languages.

Q: How do I teach the order of operations to students?

A: To teach the order of operations to students, follow these steps:

  1. Introduce the concept: Introduce the concept of the order of operations and explain its importance.
  2. Use examples: Use examples to illustrate the order of operations and how it's applied in different situations.
  3. Practice, practice, practice: Provide students with practice problems to help them apply the order of operations.
  4. Check for understanding: Check for understanding by asking students to explain the order of operations and how it's applied in different situations.

Conclusion

In conclusion, the order of operations is a crucial concept in mathematics that helps us evaluate expressions correctly. By following the order of operations, we can ensure that we're evaluating expressions correctly and avoiding errors. The order of operations has many real-world applications, and it's essential to teach it to students in a way that's easy to understand.