Indicate Whether The Sentence Or Statement Is True Or False.In The Expression $(2+4) \times 3-5$, You Should Multiply The 3 And The 5 First.Please Select The Best Answer From The Choices Provided:TF

When it comes to evaluating mathematical expressions, it's essential to follow a specific order of operations to ensure accuracy and avoid confusion. In this article, we'll explore the concept of order of operations and apply it to a given expression to determine whether a statement is true or false.

Understanding the Order of Operations

The order of operations is a set of rules that dictate 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:

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.

Evaluating the Expression

Let's apply the order of operations to the given expression:

$$(2+4) \times 3-5$$

To evaluate this expression, we need to follow the order of operations:

1. Evaluate the expression inside the parentheses: $2+4=6$
2. Multiply 6 by 3: $6 \times 3=18$
3. Subtract 5 from 18: $18-5=13$

Therefore, the final result of the expression is 13.

Is the Statement True or False?

Now that we've evaluated the expression, let's determine whether the statement is true or false:

"In the expression $(2+4) \times 3-5$, you should multiply the 3 and the 5 first."

Based on our evaluation, we can see that this statement is false. The correct order of operations is to evaluate the expression inside the parentheses first, then multiply 6 by 3, and finally subtract 5.

Conclusion

In conclusion, when evaluating mathematical expressions with multiple steps, it's essential to follow the order of operations to ensure accuracy and avoid confusion. By applying the PEMDAS rules, we can evaluate expressions like the one given and determine whether a statement is true or false.

Common Mistakes to Avoid

When working with mathematical expressions, it's easy to get confused about the order of operations. Here are some common mistakes to avoid:

• Not following the order of operations: Failing to evaluate expressions inside parentheses first, or not following the correct order of operations (PEMDAS) can lead to incorrect results.
• Not evaluating expressions inside parentheses: Failing to evaluate expressions inside parentheses can lead to incorrect results, as the expression inside the parentheses may contain multiple operations that need to be evaluated.
• Not following the correct order of operations for multiplication and division: Failing to evaluate multiplication and division operations from left to right can lead to incorrect results.

Real-World Applications

Understanding the order of operations is crucial in many real-world applications, such as:

• Science and engineering: When working with complex mathematical models, it's essential to follow the order of operations to ensure accuracy and avoid confusion.
• Finance: When working with financial calculations, it's essential to follow the order of operations to ensure accuracy and avoid confusion.
• Computer programming: When writing code, it's essential to follow the order of operations to ensure accuracy and avoid confusion.

Final Thoughts

In our previous article, we explored the concept of order of operations and applied it to a given expression. In this article, we'll answer some frequently asked questions about the order of operations.

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 when there are 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 ensures that mathematical expressions are evaluated consistently and accurately. Without the order of operations, mathematical expressions could be evaluated in different ways, leading to confusion and errors.

Q: What happens if I don't follow the order of operations?

A: If you don't follow the order of operations, you may get incorrect results. For example, if you have the expression $3 \times 2 + 4$, you may evaluate it as $3 \times 2 = 6$ and then add 4, resulting in $6 + 4 = 10$. However, if you follow the order of operations, you would evaluate the expression as $3 \times 2 = 6$ and then add 4, resulting in $6 + 4 = 10$. But if you had the expression $3 \times (2 + 4)$, you would evaluate it as $2 + 4 = 6$ and then multiply 3 by 6, resulting in $3 \times 6 = 18$. If you don't follow the order of operations, you may get the wrong result.

Q: Can I use the order of operations for expressions with multiple parentheses?

A: Yes, you can use the order of operations for expressions with multiple parentheses. When there are multiple parentheses, you should evaluate the expressions inside the innermost parentheses first, and then work your way outwards.

Q: What about expressions with exponents?

A: When there are exponents in an expression, you should evaluate them next after evaluating any expressions inside parentheses. For example, if you have the expression $2^3 \times 4$, you would evaluate the exponent first, resulting in $2^3 = 8$, and then multiply 8 by 4, resulting in $8 \times 4 = 32$.

Q: Can I use the order of operations for expressions with fractions?

A: Yes, you can use the order of operations for expressions with fractions. When there are fractions in an expression, you should evaluate them as you would any other mathematical operation.

Q: What about expressions with decimals?

A: When there are decimals in an expression, you should evaluate them as you would any other mathematical operation.

Q: Can I use the order of operations for expressions with variables?

A: Yes, you can use the order of operations for expressions with variables. When there are variables in an expression, you should evaluate them as you would any other mathematical operation.

Q: What about expressions with negative numbers?

A: When there are negative numbers in an expression, you should evaluate them as you would any other mathematical operation.

Q: Can I use the order of operations for expressions with mixed numbers?

A: Yes, you can use the order of operations for expressions with mixed numbers. When there are mixed numbers in an expression, you should evaluate them as you would any other mathematical operation.

Q: What about expressions with complex numbers?

A: When there are complex numbers in an expression, you should evaluate them as you would any other mathematical operation.

Conclusion

In conclusion, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. By following the PEMDAS rules, we can ensure accuracy and avoid confusion when evaluating mathematical expressions. Remember to evaluate expressions inside parentheses first, then follow the correct order of operations for multiplication and division, and finally evaluate any addition and subtraction operations from left to right.