Simplify The Expression:${ 12x - \frac{1}{5}{3y - 4[2x - 7(x - Y)]} }$

Introduction

In this article, we will simplify the given mathematical expression step by step. The expression is a combination of variables, constants, and operations, and it requires careful analysis to simplify it. We will use the order of operations (PEMDAS) to simplify the expression.

The Expression

The given expression is:

${ 12x - \frac{1}{5}\{3y - 4[2x - 7(x - y)]\} }$

Step 1: Simplify the Innermost Bracket

The innermost bracket is ${ 2x - 7(x - y) }$. We will simplify this expression first.

${ 2x - 7(x - y) }$

Using the distributive property, we can rewrite the expression as:

${ 2x - 7x + 7y }$

Combining like terms, we get:

${ -5x + 7y }$

Step 2: Simplify the Expression Inside the Curly Brackets

Now, we will simplify the expression inside the curly brackets:

${ 3y - 4(-5x + 7y) }$

Using the distributive property, we can rewrite the expression as:

${ 3y + 20x - 28y }$

Combining like terms, we get:

${ 20x - 25y }$

Step 3: Simplify the Expression Inside the Fraction

Now, we will simplify the expression inside the fraction:

${ \frac{1}{5}(20x - 25y) }$

Using the distributive property, we can rewrite the expression as:

${ \frac{20}{5}x - \frac{25}{5}y }$

Simplifying further, we get:

${ 4x - 5y }$

Step 4: Simplify the Final Expression

Now, we will simplify the final expression:

${ 12x - (4x - 5y) }$

Using the distributive property, we can rewrite the expression as:

${ 12x - 4x + 5y }$

Combining like terms, we get:

${ 8x + 5y }$

Conclusion

In this article, we simplified the given mathematical expression step by step. We used the order of operations (PEMDAS) to simplify the expression. The final simplified expression is:

${ 8x + 5y }$

Key Takeaways

• The order of operations (PEMDAS) is used to simplify mathematical expressions.
• The distributive property is used to simplify expressions with multiple terms.
• Combining like terms is used to simplify expressions with multiple terms.

Frequently Asked Questions

• What is the order of operations (PEMDAS)?
  • The order of operations (PEMDAS) is a set of rules used to simplify mathematical expressions. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• How do I simplify a mathematical expression?
  • To simplify a mathematical expression, you need to follow the order of operations (PEMDAS). First, simplify the expressions inside the parentheses. Then, simplify the expressions with exponents. Finally, simplify the expressions with multiplication and division, and addition and subtraction.
• What is the distributive property?
  • The distributive property is a rule used to simplify expressions with multiple terms. It states that a single term can be distributed to multiple terms.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions
  Simplify the Expression: A Q&A Guide =====================================

Introduction

In our previous article, we simplified the given mathematical expression step by step. In this article, we will answer some frequently asked questions related to simplifying mathematical expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules used to simplify mathematical expressions. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I simplify a mathematical expression?

A: To simplify a mathematical expression, you need to follow the order of operations (PEMDAS). First, simplify the expressions inside the parentheses. Then, simplify the expressions with exponents. Finally, simplify the expressions with multiplication and division, and addition and subtraction.

Q: What is the distributive property?

A: The distributive property is a rule used to simplify expressions with multiple terms. It states that a single term can be distributed to multiple terms.

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, you need to multiply the single term to each of the multiple terms. For example, if you have the expression 2(x + 3), you can use the distributive property to simplify it as 2x + 6.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms is the process of adding or subtracting terms that have the same variable and coefficient. Simplifying an expression is the process of reducing an expression to its simplest form by combining like terms, using the distributive property, and following the order of operations.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to follow the same steps as simplifying an expression with integers. First, simplify the expressions inside the parentheses. Then, simplify the expressions with exponents. Finally, simplify the expressions with multiplication and division, and addition and subtraction.

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

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I simplify an expression with variables and constants?

A: To simplify an expression with variables and constants, you need to follow the same steps as simplifying an expression with integers. First, simplify the expressions inside the parentheses. Then, simplify the expressions with exponents. Finally, simplify the expressions with multiplication and division, and addition and subtraction.

Q: What is the importance of simplifying mathematical expressions?

A: Simplifying mathematical expressions is important because it helps to reduce the complexity of an expression, making it easier to understand and work with. It also helps to identify patterns and relationships between variables and constants.

Conclusion

In this article, we answered some frequently asked questions related to simplifying mathematical expressions. We hope that this article has provided you with a better understanding of the order of operations, the distributive property, and how to simplify expressions with variables and constants.

Key Takeaways

• The order of operations (PEMDAS) is used to simplify mathematical expressions.
• The distributive property is used to simplify expressions with multiple terms.
• Combining like terms is used to simplify expressions with multiple terms.
• Simplifying an expression with fractions is the same as simplifying an expression with integers.
• A variable is a letter or symbol that represents a value that can change.
• A constant is a value that does not change.

Frequently Asked Questions

• What is the order of operations (PEMDAS)?
  • The order of operations (PEMDAS) is a set of rules used to simplify mathematical expressions. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• How do I simplify a mathematical expression?
  • To simplify a mathematical expression, you need to follow the order of operations (PEMDAS). First, simplify the expressions inside the parentheses. Then, simplify the expressions with exponents. Finally, simplify the expressions with multiplication and division, and addition and subtraction.
• What is the distributive property?
  • The distributive property is a rule used to simplify expressions with multiple terms. It states that a single term can be distributed to multiple terms.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions