Simplify The Expression: $ (2x \times 7) , \text{cm} $

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. When dealing with algebraic expressions, we often come across terms that can be combined or simplified using various mathematical operations. In this article, we will focus on simplifying the given expression: $(2x \times 7) \, \text{cm}$. We will break down the steps involved in simplifying this expression and provide a clear understanding of the mathematical concepts used.

Understanding the Expression

The given expression is $(2x \times 7) \, \text{cm}$. To simplify this expression, we need to understand the mathematical operations involved. The expression consists of two terms: $2x$ and $7$. The multiplication symbol $\times$ indicates that we need to multiply these two terms together.

Applying the Order of Operations

When simplifying expressions, it's essential to follow the order of operations (PEMDAS):

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.

In this case, we have a multiplication operation between $2x$ and $7$. Therefore, we will apply the multiplication operation first.

Simplifying the Expression

To simplify the expression, we will multiply $2x$ and $7$ together:

$(2x \times 7) = 2x \times 7$

Using the distributive property of multiplication over addition, we can rewrite the expression as:

$2x \times 7 = (2 \times 7) \times x$

Now, we can simplify the expression further by multiplying $2$ and $7$ together:

$(2 \times 7) = 14$

Therefore, the simplified expression is:

$14x$

Conclusion

In this article, we simplified the expression $(2x \times 7) \, \text{cm}$ using the order of operations and the distributive property of multiplication over addition. We broke down the steps involved in simplifying the expression and provided a clear understanding of the mathematical concepts used. By following these steps, we can simplify complex expressions and solve problems efficiently and accurately.

Frequently Asked Questions

• What is the order of operations in mathematics? The order of operations is a set of rules that tells us which operations to perform first when simplifying expressions. The order of operations is: parentheses, exponents, multiplication and division, and addition and subtraction.
• How do I simplify an expression using the distributive property? To simplify an expression using the distributive property, you need to multiply each term inside the parentheses by the term outside the parentheses.
• What is the distributive property of multiplication over addition? The distributive property of multiplication over addition states that a single term can be multiplied by each term inside the parentheses separately.

Additional Resources

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

Final Thoughts

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations and using the distributive property of multiplication over addition, we can simplify complex expressions and solve problems with confidence.

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Introduction

In our previous article, we simplified the expression $(2x \times 7) \, \text{cm}$ using the order of operations and the distributive property of multiplication over addition. In this article, we will answer some frequently asked questions related to simplifying expressions and provide additional resources for further learning.

Q&A

Q: What is the order of operations in mathematics?

A: The order of operations is a set of rules that tells us which operations to perform first when simplifying expressions. The order of operations is: parentheses, exponents, multiplication and division, and addition and subtraction.

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

A: To simplify an expression using the distributive property, you need to multiply each term inside the parentheses by the term outside the parentheses. For example, if you have the expression $(2x + 3) \times 4$, you would multiply each term inside the parentheses by 4: $(2x \times 4) + (3 \times 4)$.

Q: What is the distributive property of multiplication over addition?

A: The distributive property of multiplication over addition states that a single term can be multiplied by each term inside the parentheses separately. For example, if you have the expression $(2x + 3) \times 4$, you can multiply 4 by each term inside the parentheses: $(2x \times 4) + (3 \times 4)$.

Q: How do I simplify an expression with multiple operations?

A: To simplify an expression with multiple operations, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

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. For example, in the expression $2x$, $x$ is a variable because its value can change. In contrast, the number 2 is a constant because its value does not change.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to follow the rules of fraction arithmetic. First, simplify each fraction separately. Then, combine the fractions by finding a common denominator.

Additional Resources

• Khan Academy: Simplifying Expressions
• Mathway: Simplifying Expressions
• Wolfram Alpha: Simplifying Expressions
• MIT OpenCourseWare: Algebra
• Purplemath: Simplifying Expressions

Final Thoughts

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations and using the distributive property of multiplication over addition, we can simplify complex expressions and solve problems with confidence. We hope this Q&A article has provided you with a better understanding of simplifying expressions and has helped you to improve your math skills.

Common Mistakes to Avoid

• Not following the order of operations
• Not using the distributive property of multiplication over addition
• Not simplifying fractions
• Not combining like terms
• Not checking for errors in the final answer

Tips for Success

• Practice simplifying expressions regularly
• Use online resources and tools to help you simplify expressions
• Break down complex expressions into smaller, more manageable parts
• Check your work carefully to avoid errors
• Ask for help if you are struggling with a particular expression

Conclusion

Simplifying expressions is a crucial skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations and using the distributive property of multiplication over addition, we can simplify complex expressions and solve problems with confidence. We hope this Q&A article has provided you with a better understanding of simplifying expressions and has helped you to improve your math skills.