Solve The Problem Below And Enter Your Answer In The Space Provided:$(6+2)+(6+3)+(8+5) = ?$Answer Here: ________

Understanding the Problem

The given problem involves evaluating an expression that consists of multiple addition operations. The expression is: $(6+2)+(6+3)+(8+5) = ?$

To solve this problem, we need to follow the order of operations (PEMDAS) and evaluate the expressions inside the parentheses first.

Evaluating Expressions Inside Parentheses

The expression inside the first parentheses is: $6+2$

To evaluate this expression, we simply add 6 and 2 together.

Evaluating 6+2

$$6+2 = 8$$

So, the expression inside the first parentheses evaluates to 8.

Evaluating the Next Expression

The expression inside the second parentheses is: $6+3$

To evaluate this expression, we simply add 6 and 3 together.

Evaluating 6+3

$$6+3 = 9$$

So, the expression inside the second parentheses evaluates to 9.

Evaluating the Final Expression

The expression inside the third parentheses is: $8+5$

To evaluate this expression, we simply add 8 and 5 together.

Evaluating 8+5

$$8+5 = 13$$

So, the expression inside the third parentheses evaluates to 13.

Combining the Results

Now that we have evaluated all the expressions inside the parentheses, we can combine the results to get the final answer.

Combining the Results

$$(6+2) = 8$$

$$(6+3) = 9$$

$$(8+5) = 13$$

Adding these results together, we get:

$$8 + 9 + 13 = 30$$

Therefore, the final answer is:

The Final Answer

The final answer is: 30

Conclusion

In this problem, we evaluated an expression that consisted of multiple addition operations. We followed the order of operations (PEMDAS) and evaluated the expressions inside the parentheses first. Then, we combined the results to get the final answer. This problem demonstrates the importance of following the order of operations when evaluating mathematical expressions.

Frequently Asked Questions

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when evaluating mathematical expressions. PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
3. Multiplication and Division: Evaluate any 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 it important to follow the order of operations?

A: Following the order of operations is crucial when evaluating mathematical expressions because it ensures that we perform the operations in the correct order. If we don't follow the order of operations, we may get incorrect results.

Q: How do I evaluate expressions with multiple addition operations?

A: To evaluate expressions with multiple addition operations, follow these steps:

1. Evaluate any expressions inside parentheses first.
2. Evaluate any exponential expressions next (if present).
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have multiple sets of parentheses in an expression?

A: If you have multiple sets of parentheses in an expression, evaluate the innermost parentheses first, then work your way outwards.

Q: Can I use a calculator to evaluate expressions with addition operations?

A: Yes, you can use a calculator to evaluate expressions with addition operations. However, it's still important to understand the order of operations and how to evaluate expressions manually.

Q: How do I evaluate expressions with variables?

A: To evaluate expressions with variables, follow these steps:

1. Evaluate any expressions inside parentheses first.
2. Evaluate any exponential expressions next (if present).
3. Evaluate any multiplication and division operations from left to right.
4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have a negative number in an expression?

A: If you have a negative number in an expression, remember to follow the order of operations. For example, if you have the expression -3 + 2, you would first evaluate the addition operation, then apply the negative sign.

Q: Can I use a calculator to evaluate expressions with variables?

A: Yes, you can use a calculator to evaluate expressions with variables. However, it's still important to understand the order of operations and how to evaluate expressions manually.

Common Mistakes to Avoid

1. Not following the order of operations

Failing to follow the order of operations can lead to incorrect results.

2. Not evaluating expressions inside parentheses first

Failing to evaluate expressions inside parentheses first can lead to incorrect results.

3. Not evaluating exponential expressions next

Failing to evaluate exponential expressions next can lead to incorrect results.

4. Not evaluating multiplication and division operations from left to right

Failing to evaluate multiplication and division operations from left to right can lead to incorrect results.

5. Not evaluating addition and subtraction operations from left to right

Failing to evaluate addition and subtraction operations from left to right can lead to incorrect results.

Conclusion

Evaluating expressions with addition operations requires following the order of operations (PEMDAS). By understanding the order of operations and how to evaluate expressions manually, you can avoid common mistakes and get accurate results.