Use The Order Of Operations To Solve The Problem Below:$20 - 7 + 7 - 15 \div 3$

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 a crucial concept in mathematics that ensures we perform calculations in the correct sequence, avoiding confusion and errors. 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 Problem

Now, let's apply the order of operations to the given problem:

$$20 - 7 + 7 - 15 \div 3$$

To solve this problem, we need to follow the order of operations:

1. Parentheses: There are no expressions inside parentheses, so we can move on to the next step.
2. Exponents: There are no exponential expressions, so we can move on to the next step.
3. Multiplication and Division: We need to evaluate the division operation first. The expression is $15 \div 3$, which equals $5$.
4. Addition and Subtraction: Now, we can evaluate the addition and subtraction operations from left to right. The expression becomes:

$$20 - 7 + 7 - 5$$

Evaluating the Expression

Now, let's evaluate the expression step by step:

1. Subtract 7 from 20: $20 - 7 = 13$
2. Add 7 to 13: $13 + 7 = 20$
3. Subtract 5 from 20: $20 - 5 = 15$

The final answer is $\boxed{15}$.

Why the Order of Operations is Important

The order of operations is essential in mathematics because it helps us evaluate expressions correctly. Without the order of operations, mathematical expressions can be ambiguous, leading to confusion and errors. For example, consider the expression $3 \times 2 + 4$. Without the order of operations, we might evaluate it as $3 \times 2 = 6$, and then add 4, resulting in $10$. However, using the order of operations, we evaluate the multiplication first, resulting in $6$, and then add 4, resulting in $10$. This example illustrates the importance of following the order of operations to ensure accurate results.

Real-World Applications of the Order of Operations

The order of operations has numerous real-world applications in various fields, including:

• Science: In scientific calculations, the order of operations is crucial in evaluating complex expressions, such as those involving exponents, logarithms, and trigonometric functions.
• Engineering: In engineering, the order of operations is essential in designing and analyzing complex systems, such as electrical circuits, mechanical systems, and computer networks.
• Finance: In finance, the order of operations is critical in evaluating financial expressions, such as those involving interest rates, investments, and currency exchange rates.

Conclusion

In conclusion, the order of operations is a fundamental concept in mathematics that helps us evaluate expressions correctly. By following the order of operations, we can ensure accurate results and avoid confusion and errors. The order of operations has numerous real-world applications in various fields, making it an essential tool for anyone working with mathematical expressions.

Additional Resources

For further learning, here are some additional resources:

• Math textbooks: Consult a math textbook for a comprehensive explanation of the order of operations.
• Online resources: Visit online resources, such as Khan Academy, Mathway, or Wolfram Alpha, for interactive lessons and practice exercises.
• Practice problems: Practice solving mathematical expressions using the order of operations to reinforce your understanding.

By following the order of operations and practicing with real-world examples, you can become proficient in evaluating mathematical expressions and apply this knowledge to various fields.

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 a crucial concept in mathematics that ensures we perform calculations in the correct sequence, avoiding confusion and errors.

Q: What is the acronym PEMDAS?

A: PEMDAS is an acronym that 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 the order of operations important?

A: The order of operations is essential in mathematics because it helps us evaluate expressions correctly. Without the order of operations, mathematical expressions can be ambiguous, leading to confusion and errors.

Q: How do I apply the order of operations to a mathematical expression?

A: To apply the order of operations to a mathematical expression, follow these steps:

1. Evaluate any expressions inside parentheses.
2. Evaluate any exponential expressions.
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 there are multiple operations with the same precedence?

A: If there are multiple operations with the same precedence, evaluate them from left to right. For example, in the expression $3 \times 2 + 4$, we evaluate the multiplication first, resulting in $6$, and then add $4$, resulting in $10$.

Q: Can I use the order of operations to simplify complex expressions?

A: Yes, the order of operations can be used to simplify complex expressions. By following the order of operations, you can break down complex expressions into simpler ones, making them easier to evaluate.

Q: Are there any exceptions to the order of operations?

A: Yes, there are some exceptions to the order of operations. For example, in some cases, the order of operations may be modified to accommodate specific mathematical operations, such as the order of operations for trigonometric functions.

Q: How can I practice using the order of operations?

A: You can practice using the order of operations by working through mathematical exercises and problems. You can also use online resources, such as Khan Academy, Mathway, or Wolfram Alpha, to practice and reinforce your understanding.

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

A: The order of operations has numerous real-world applications in various fields, including:

• Science: In scientific calculations, the order of operations is crucial in evaluating complex expressions, such as those involving exponents, logarithms, and trigonometric functions.
• Engineering: In engineering, the order of operations is essential in designing and analyzing complex systems, such as electrical circuits, mechanical systems, and computer networks.
• Finance: In finance, the order of operations is critical in evaluating financial expressions, such as those involving interest rates, investments, and currency exchange rates.

Q: Can I use the order of operations to evaluate expressions with multiple variables?

A: Yes, the order of operations can be used to evaluate expressions with multiple variables. By following the order of operations, you can evaluate expressions with multiple variables in a step-by-step manner.

Q: Are there any online resources that can help me learn the order of operations?

A: Yes, there are many online resources that can help you learn the order of operations, including:

• Khan Academy: Khan Academy offers interactive lessons and practice exercises on the order of operations.
• Mathway: Mathway is an online math problem solver that can help you evaluate mathematical expressions and practice using the order of operations.
• Wolfram Alpha: Wolfram Alpha is a powerful online calculator that can help you evaluate mathematical expressions and practice using the order of operations.

By following the order of operations and practicing with real-world examples, you can become proficient in evaluating mathematical expressions and apply this knowledge to various fields.