Simplify The Expression:$6 + 2 \times 8 - 5$ Use The Order Of Operations: - Parentheses- Exponents- Multiplication And Division (from Left To Right)- Addition And Subtraction (from Left To Right)

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Understanding the Order of Operations

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. This is especially important in mathematics, as it helps us to evaluate expressions accurately and avoid confusion. The order of operations is often remembered using the acronym PEMDAS, which stands for:

  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.

Applying the Order of Operations to the Given Expression

Now that we understand the order of operations, let's apply it to the given expression: 6+2×8−56 + 2 \times 8 - 5. We will follow the order of operations to simplify the expression.

Step 1: Evaluate Expressions Inside Parentheses

In this case, there are no expressions inside parentheses, so we can move on to the next step.

Step 2: Evaluate Exponential Expressions

There are no exponential expressions in the given expression, so we can move on to the next step.

Step 3: Evaluate Multiplication and Division Operations

The expression contains a multiplication operation: 2×82 \times 8. We will evaluate this operation first.

2×8=162 \times 8 = 16

So, the expression becomes: 6+16−56 + 16 - 5

Step 4: Evaluate Addition and Subtraction Operations

Now that we have evaluated the multiplication operation, we can move on to the addition and subtraction operations. We will evaluate these operations from left to right.

First, we will add 6 and 16:

6+16=226 + 16 = 22

Then, we will subtract 5 from 22:

22−5=1722 - 5 = 17

Therefore, the simplified expression is: 1717

Conclusion

In this article, we applied the order of operations to simplify the expression: 6+2×8−56 + 2 \times 8 - 5. We followed the order of operations, which is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. By applying the order of operations, we were able to simplify the expression and arrive at the final answer: 1717.

Common Mistakes to Avoid

When simplifying expressions using the order of operations, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Not following the order of operations: Make sure to follow the order of operations carefully, as skipping or misordering operations can lead to incorrect results.
  • Not evaluating expressions inside parentheses first: Expressions inside parentheses should be evaluated first, as they take precedence over other operations.
  • Not evaluating exponential expressions next: Exponential expressions should be evaluated next, as they take precedence over multiplication and division operations.
  • Not evaluating multiplication and division operations from left to right: Multiplication and division operations should be evaluated from left to right, as they have the same precedence.
  • Not evaluating addition and subtraction operations from left to right: Addition and subtraction operations should be evaluated from left to right, as they have the same precedence.

Practice Problems

To practice simplifying expressions using the order of operations, try the following problems:

  1. Simplify the expression: 3+2×4−13 + 2 \times 4 - 1
  2. Simplify the expression: 12−3×2+512 - 3 \times 2 + 5
  3. Simplify the expression: 9+4×3−29 + 4 \times 3 - 2

Answer Key

  1. 3+2×4−1=3+8−1=103 + 2 \times 4 - 1 = 3 + 8 - 1 = 10
  2. 12−3×2+5=12−6+5=1112 - 3 \times 2 + 5 = 12 - 6 + 5 = 11
  3. 9+4×3−2=9+12−2=199 + 4 \times 3 - 2 = 9 + 12 - 2 = 19

Conclusion

Frequently Asked Questions

In this article, we will answer some frequently asked questions about simplifying expressions using the order of operations.

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 order of operations is often remembered using the acronym PEMDAS, which stands for:

  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 it important to follow the order of operations?

A: Following the order of operations is important because it helps us to evaluate expressions accurately and avoid confusion. If we don't follow the order of operations, we may get incorrect results.

Q: What happens if there are no expressions inside parentheses?

A: If there are no expressions inside parentheses, we can move on to the next step, which is to evaluate any exponential expressions.

Q: What happens if there are no exponential expressions?

A: If there are no exponential expressions, we can move on to the next step, which is to evaluate any multiplication and division operations.

Q: What happens if there are multiple multiplication and division operations?

A: If there are multiple multiplication and division operations, we evaluate them from left to right. For example, if we have the expression 2×3+4×52 \times 3 + 4 \times 5, we would first evaluate 2×32 \times 3 and then 4×54 \times 5.

Q: What happens if there are multiple addition and subtraction operations?

A: If there are multiple addition and subtraction operations, we evaluate them from left to right. For example, if we have the expression 2+3−4+52 + 3 - 4 + 5, we would first evaluate 2+32 + 3 and then 4−54 - 5.

Q: Can I simplify expressions using the order of operations if I have a calculator?

A: Yes, you can simplify expressions using the order of operations even if you have a calculator. However, it's still important to follow the order of operations to ensure that you get the correct result.

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

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

  • Not following the order of operations
  • Not evaluating expressions inside parentheses first
  • Not evaluating exponential expressions next
  • Not evaluating multiplication and division operations from left to right
  • Not evaluating addition and subtraction operations from left to right

Practice Problems

To practice simplifying expressions using the order of operations, try the following problems:

  1. Simplify the expression: 3+2×4−13 + 2 \times 4 - 1
  2. Simplify the expression: 12−3×2+512 - 3 \times 2 + 5
  3. Simplify the expression: 9+4×3−29 + 4 \times 3 - 2

Answer Key

  1. 3+2×4−1=3+8−1=103 + 2 \times 4 - 1 = 3 + 8 - 1 = 10
  2. 12−3×2+5=12−6+5=1112 - 3 \times 2 + 5 = 12 - 6 + 5 = 11
  3. 9+4×3−2=9+12−2=199 + 4 \times 3 - 2 = 9 + 12 - 2 = 19

Conclusion

In this article, we answered some frequently asked questions about simplifying expressions using the order of operations. We discussed the importance of following the order of operations, how to handle expressions with multiple operations, and common mistakes to avoid. We also provided practice problems to help you practice simplifying expressions using the order of operations.