4 Times (5^2 - 12) - 6

Feb 26, 2025 by ADMIN 23 views

Understanding the Problem

When dealing with algebraic expressions, it's essential to follow the correct order of operations to ensure accurate results. In this article, we'll focus on solving the expression 4 times (5^2 - 12) - 6, which involves exponentiation, subtraction, multiplication, and subtraction. Our goal is to break down the problem into manageable steps and provide a clear understanding of the solution process.

The Order of Operations

To solve the given expression, we need to follow the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. 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.

Breaking Down the Expression

Now that we've covered the order of operations, let's break down the given expression into smaller parts:

4 times (5^2 - 12) - 6

We can start by evaluating the expression inside the parentheses:

5^2 - 12

Evaluating Exponents

The first step is to evaluate the exponential expression 5^2. This means multiplying 5 by itself:

5^2 = 5 × 5 = 25

Now that we have the result of the exponentiation, we can substitute it back into the original expression:

4 times (25 - 12) - 6

Subtracting Inside the Parentheses

Next, we need to evaluate the expression inside the parentheses:

25 - 12 = 13

Now that we have the result of the subtraction, we can substitute it back into the original expression:

4 times 13 - 6

Multiplying

The next step is to multiply 4 by 13:

4 × 13 = 52

Now that we have the result of the multiplication, we can substitute it back into the original expression:

52 - 6

Subtracting

Finally, we need to subtract 6 from 52:

52 - 6 = 46

Conclusion

In this article, we've walked through the process of solving the algebraic expression 4 times (5^2 - 12) - 6. By following the order of operations and breaking down the expression into smaller parts, we were able to evaluate the expression accurately. The final result is 46.

Real-World Applications

Understanding how to solve algebraic expressions is essential in various real-world applications, such as:

Science and Engineering: Algebraic expressions are used to model and solve problems in physics, engineering, and other scientific fields.
Finance: Algebraic expressions are used to calculate interest rates, investments, and other financial calculations.
Computer Science: Algebraic expressions are used in computer programming to solve problems and make decisions.

Tips and Tricks

Here are some tips and tricks to help you solve algebraic expressions:

Read the problem carefully: Make sure you understand what the problem is asking for.
Follow the order of operations: Use the PEMDAS acronym to remember the order of operations.
Break down the expression: Divide the expression into smaller parts to make it easier to solve.
Check your work: Double-check your calculations to ensure accuracy.

Common Mistakes

Here are some common mistakes to avoid when solving algebraic expressions:

Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
Not breaking down the expression: Failing to break down the expression into smaller parts can make it difficult to solve.
Not checking your work: Failing to check your work can lead to errors and incorrect results.

Conclusion

Solving algebraic expressions is an essential skill in mathematics and has numerous real-world applications. By following the order of operations and breaking down the expression into smaller parts, you can accurately evaluate algebraic expressions. Remember to read the problem carefully, follow the order of operations, and check your work to ensure accuracy.

Understanding Algebraic Expressions

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. It's a way to represent a mathematical relationship between variables and constants.

Q: What are the different types of algebraic expressions?

A: There are several types of algebraic expressions, including:

Polynomial expressions: These are expressions that contain variables and constants, and the variables are raised to non-negative integer powers.
Rational expressions: These are expressions that contain variables and constants, and the variables are raised to non-negative integer powers, and the expression is divided by a polynomial.
Exponential expressions: These are expressions that contain variables and constants, and the variables are raised to non-negative integer powers.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow the order of operations (PEMDAS):

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: What is the difference between an equation and an expression?

A: An equation is a statement that says two expressions are equal, while an expression is a mathematical statement that contains variables and constants.

Q: How do I solve an algebraic equation?

A: To solve an algebraic equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. 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: How do I evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, you need to follow the order of operations. First, evaluate any expressions inside the parentheses, and then evaluate any exponential expressions, and finally, evaluate any multiplication and division operations from left to right.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to follow the order of operations. First, evaluate any expressions inside the parentheses, and then evaluate any exponential expressions, and finally, evaluate any multiplication and division operations from left to right.

Q: What is the difference between a rational expression and a polynomial expression?

A: A rational expression is an expression that contains variables and constants, and the variables are raised to non-negative integer powers, and the expression is divided by a polynomial. A polynomial expression is an expression that contains variables and constants, and the variables are raised to non-negative integer powers.

Conclusion

Algebraic expressions are a fundamental concept in mathematics, and they can be intimidating at first. However, with practice and patience, you can become proficient in solving them. By following the order of operations and simplifying expressions, you can accurately evaluate algebraic expressions. Remember to read the problem carefully, follow the order of operations, and check your work to ensure accuracy.