Applying Order of Operations to the Given Expression

Oct 13, 2025 by leolavanderia.com.br 32 views

Introduction

In algebra, expressions can become complex and difficult to solve. One way to simplify these expressions is by applying the rules of order of operations. This concept is crucial in mathematics, as it helps us evaluate expressions with multiple operations in a consistent and predictable manner. In this article, we will explore the rules of order of operations and apply them to simplify the expression $$2 + 3 - 4 + (5 \times 4)$$.

What is Order of Operations?

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 acronym PEMDAS is commonly used to remember the order of operations:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Applying Order of Operations to the Given Expression

Now that we have a good understanding of the order of operations, let's apply these rules to simplify the expression $$2 + 3 - 4 + (5 \times 4)$$.

Step 1: Evaluate Expressions Inside Parentheses

The first step is to evaluate the expression inside the parentheses: $$5 \times 4$$. According to the order of operations, we need to perform multiplication before addition and subtraction.

# Evaluate the expression inside the parentheses
result_inside_parentheses = 5 * 4
print(result_inside_parentheses)

The result of the expression inside the parentheses is 20.

Step 2: Replace the Expression Inside the Parentheses with the Result

Now that we have evaluated the expression inside the parentheses, we can replace it with the result in the original expression: $$2 + 3 - 4 + 20$$.

Step 3: Evaluate Exponents (None in this Case)

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

Step 4: Evaluate Multiplication and Division (None in this Case)

Similarly, there are no multiplication or division operations in the given expression, so we can move on to the next step.

Step 5: Evaluate Addition and Subtraction

Now that we have evaluated all the operations inside the parentheses, we can perform the addition and subtraction operations from left to right.

# Evaluate the addition and subtraction operations
result = 2 + 3 - 4 + 20
print(result)

The final result of the expression is 21.

Conclusion

In this article, we applied the rules of order of operations to simplify the expression $$2 + 3 - 4 + (5 \times 4)$$. By following the order of operations, we were able to evaluate the expression step by step and arrive at the final result. The order of operations is a crucial concept in mathematics, and understanding it can help us simplify complex expressions and solve problems more efficiently.

Answer

The correct answer is A. 21.

Additional Examples

Here are a few more examples of applying the order of operations to simplify expressions:

$3 + 2 \times 4 - 1$
$10 - 2 + 3 \times 2$
$4 + 2 - 3 \times 1$

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 acronym PEMDAS is commonly used to remember the order of operations:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate 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 the order of operations important?

A: The order of operations is important because it helps us evaluate expressions with multiple operations in a consistent and predictable manner. Without the order of operations, expressions could be evaluated differently depending on the order in which we perform the operations.

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

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

Evaluate expressions inside parentheses first.
Evaluate any exponential expressions next.
Evaluate multiplication and division operations from left to right.
Finally, evaluate any addition and subtraction operations from left to right.

Q: What if I have multiple operations with the same precedence (e.g., two multiplication operations)?

A: If you have multiple operations with the same precedence, evaluate them from left to right. For example, if you have the expression $$2 \times 3 \times 4$$, you would evaluate it as follows:

$2 \times 3 = 6$
$6 \times 4 = 24$

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

A: Yes, you can use the order of operations to simplify expressions with fractions. For example, if you have the expression $$\frac{1}{2} + \frac{1}{3}$$, you would evaluate it as follows:

Find a common denominator (in this case, 6).
Rewrite each fraction with the common denominator: $$\frac{3}{6} + \frac{2}{6}$$
Add the fractions: $$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$

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

A: Yes, you can use the order of operations to simplify expressions with decimals. For example, if you have the expression $$2.5 + 3.2 - 1.8$$, you would evaluate it as follows:

Add 2.5 and 3.2: $$2.5 + 3.2 = 5.7$$
Subtract 1.8 from 5.7: $$5.7 - 1.8 = 3.9$$

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

A: If you have a negative number in an expression, treat it like any other number. For example, if you have the expression $$-2 + 3 - 4$$, you would evaluate it as follows:

Add 3 and -2: $$3 + (-2) = 1$$
Subtract 4 from 1: $$1 - 4 = -3$$

Conclusion

In this article, we answered some frequently asked questions about the order of operations. We covered topics such as the importance of the order of operations, how to apply it to complex expressions, and how to simplify expressions with fractions and decimals. We also discussed how to handle negative numbers in expressions. By understanding the order of operations, you can simplify complex expressions and solve problems more efficiently.