2.4 Explain To The Learners, Verbatim, How To Apply The Order Of Operation Rules For The Following Mathematical Expressions (2.4.1-2.4.5):$\[ \begin{array}{|l|l|} \hline 2.4.1 & 10 + 4 - (5 - 2) = \square \\ \hline 2.4.2 & 20 - 10 - 8 + 2 = \square
Understanding the Order of Operations
The order of operations is a set of rules that helps us evaluate mathematical expressions in the correct order. It is essential to follow these rules to avoid confusion and ensure that mathematical expressions are evaluated consistently. In this article, we will explore the order of operations rules and apply them to various mathematical expressions.
The Order of Operations Rules
The order of operations rules are as follows:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Applying the Order of Operations Rules
2.4.1: 10 + 4 - (5 - 2)
To evaluate this expression, we need to follow the order of operations rules.
- Step 1: Evaluate expressions inside parentheses
- Inside the parentheses, we have 5 - 2 = 3
- So, the expression becomes 10 + 4 - 3
- Step 2: Evaluate any exponential expressions
- There are no exponential expressions in this expression
- Step 3: Evaluate any multiplication and division operations
- There are no multiplication and division operations in this expression
- Step 4: Evaluate any addition and subtraction operations
- Finally, we evaluate the addition and subtraction operations from left to right
- 10 + 4 = 14
- 14 - 3 = 11
Therefore, the value of the expression 10 + 4 - (5 - 2) is 11.
2.4.2: 20 - 10 - 8 + 2
To evaluate this expression, we need to follow the order of operations rules.
- Step 1: Evaluate expressions inside parentheses
- There are no expressions inside parentheses in this expression
- Step 2: Evaluate any exponential expressions
- There are no exponential expressions in this expression
- Step 3: Evaluate any multiplication and division operations
- There are no multiplication and division operations in this expression
- Step 4: Evaluate any addition and subtraction operations
- Finally, we evaluate the addition and subtraction operations from left to right
- 20 - 10 = 10
- 10 - 8 = 2
- 2 + 2 = 4
Therefore, the value of the expression 20 - 10 - 8 + 2 is 4.
2.4.3: 3 × 2 + 12 - 8
To evaluate this expression, we need to follow the order of operations rules.
- Step 1: Evaluate expressions inside parentheses
- There are no expressions inside parentheses in this expression
- Step 2: Evaluate any exponential expressions
- There are no exponential expressions in this expression
- Step 3: Evaluate any multiplication and division operations
- 3 × 2 = 6
- So, the expression becomes 6 + 12 - 8
- Step 4: Evaluate any addition and subtraction operations
- Finally, we evaluate the addition and subtraction operations from left to right
- 6 + 12 = 18
- 18 - 8 = 10
Therefore, the value of the expression 3 × 2 + 12 - 8 is 10.
2.4.4: 15 - 3 + 2 × 4
To evaluate this expression, we need to follow the order of operations rules.
- Step 1: Evaluate expressions inside parentheses
- There are no expressions inside parentheses in this expression
- Step 2: Evaluate any exponential expressions
- There are no exponential expressions in this expression
- Step 3: Evaluate any multiplication and division operations
- 2 × 4 = 8
- So, the expression becomes 15 - 3 + 8
- Step 4: Evaluate any addition and subtraction operations
- Finally, we evaluate the addition and subtraction operations from left to right
- 15 - 3 = 12
- 12 + 8 = 20
Therefore, the value of the expression 15 - 3 + 2 × 4 is 20.
2.4.5: 24 ÷ 3 + 2 - 8
To evaluate this expression, we need to follow the order of operations rules.
- Step 1: Evaluate expressions inside parentheses
- There are no expressions inside parentheses in this expression
- Step 2: Evaluate any exponential expressions
- There are no exponential expressions in this expression
- Step 3: Evaluate any multiplication and division operations
- 24 ÷ 3 = 8
- So, the expression becomes 8 + 2 - 8
- Step 4: Evaluate any addition and subtraction operations
- Finally, we evaluate the addition and subtraction operations from left to right
- 8 + 2 = 10
- 10 - 8 = 2
Therefore, the value of the expression 24 ÷ 3 + 2 - 8 is 2.
Q: What is the order of operations?
A: The order of operations is a set of rules that helps us evaluate mathematical expressions in the correct order. It is essential to follow these rules to avoid confusion and ensure that mathematical expressions are evaluated consistently.
Q: What are the order of operations rules?
A: The order of operations rules are as follows:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: Why is it essential to follow the order of operations rules?
A: Following the order of operations rules ensures that mathematical expressions are evaluated consistently and accurately. It helps to avoid confusion and ensures that the correct answer is obtained.
Q: What happens if I don't follow the order of operations rules?
A: If you don't follow the order of operations rules, you may obtain an incorrect answer. This can lead to confusion and errors in mathematical calculations.
Q: How do I apply the order of operations rules to a mathematical expression?
A: To apply the order of operations rules to a mathematical expression, follow these steps:
- Evaluate expressions inside parentheses first.
- Evaluate any exponential expressions next.
- Evaluate any multiplication and division operations from left to right.
- Finally, evaluate any addition and subtraction operations from left to right.
Q: What are some examples of mathematical expressions that require the order of operations rules?
A: Here are some examples of mathematical expressions that require the order of operations rules:
- 10 + 4 - (5 - 2)
- 20 - 10 - 8 + 2
- 3 × 2 + 12 - 8
- 15 - 3 + 2 × 4
- 24 ÷ 3 + 2 - 8
Q: How do I evaluate expressions with multiple operations?
A: To evaluate expressions with multiple operations, follow the order of operations rules. Evaluate expressions inside parentheses first, then evaluate any exponential expressions, followed by any multiplication and division operations, and finally evaluate any addition and subtraction operations.
Q: What are some common mistakes to avoid when applying the order of operations rules?
A: Here are some common mistakes to avoid when applying the order of operations rules:
- 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.
Q: How can I practice applying the order of operations rules?
A: You can practice applying the order of operations rules by working through mathematical exercises and problems. Start with simple expressions and gradually move on to more complex ones. You can also use online resources and tools to help you practice and improve your skills.
Q: What are some real-world applications of the order of operations rules?
A: The order of operations rules have many real-world applications, including:
- Scientific calculations
- Financial calculations
- Engineering calculations
- Computer programming
In conclusion, the order of operations rules are essential to evaluate mathematical expressions correctly. By following these rules, you can ensure that mathematical expressions are evaluated consistently and accurately.