Write The Product Of The Following Expression:$\[-10(4.5v + 7) = \square\\]

Understanding the Expression

The given expression is a linear equation in the form of $-10(4.5v + 7)$. To write the product of this expression, we need to follow the order of operations (PEMDAS) and simplify the equation.

Applying the Order of Operations

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 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.

Simplifying the Expression

In the given expression, $-10(4.5v + 7)$, we have a multiplication operation inside the parentheses. To simplify the expression, we need to multiply the value outside the parentheses, which is $-10$, by the expression inside the parentheses, which is $(4.5v + 7)$.

Distributive Property

To multiply a value outside the parentheses by an expression inside the parentheses, we can use the distributive property. The distributive property states that for any numbers $a$, $b$, and $c$, the following equation holds:

$a(b + c) = ab + ac$

Using this property, we can rewrite the expression as:

$-10(4.5v + 7) = -10(4.5v) + (-10)(7)$

Simplifying the Expression Further

Now, we can simplify the expression further by multiplying the values inside the parentheses.

$-10(4.5v) = -45v$ $(-10)(7) = -70$

Writing the Product of the Expression

Therefore, the product of the given expression is:

$-45v - 70$

Conclusion

In this article, we learned how to write the product of a given expression using the distributive property and the order of operations. We simplified the expression step by step and arrived at the final product, which is $-45v - 70$. This result can be used in various mathematical applications, such as solving linear equations and inequalities.

Frequently Asked Questions

• What is the order of operations? 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 stands for: 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, multiply the value outside the parentheses by the expression inside the parentheses, and then simplify the resulting expression.

Additional Resources

• For more information on the order of operations, visit www.mathway.com.
• For more information on the distributive property, visit www.khanacademy.org.

Final Thoughts

In conclusion, writing the product of a given expression requires a clear understanding of the order of operations and the distributive property. By following these rules and simplifying the expression step by step, we can arrive at the final product and use it in various mathematical applications.

Understanding the Basics

Writing the product of a given expression can be a challenging task, especially for those who are new to algebra. However, with a clear understanding of the order of operations and the distributive property, anyone can simplify an expression and arrive at the final product.

Q&A Session

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 stands for: 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, multiply the value outside the parentheses by the expression inside the parentheses, and then simplify the resulting expression.

Q: What is the distributive property?

A: The distributive property is a mathematical rule that states that for any numbers $a$, $b$, and $c$, the following equation holds:

$a(b + c) = ab + ac$

This property allows us to multiply a value outside the parentheses by an expression inside the parentheses.

Q: How do I apply the distributive property to a given expression?

A: To apply the distributive property to a given expression, follow these steps:

1. Identify the value outside the parentheses and the expression inside the parentheses.
2. Multiply the value outside the parentheses by each term inside the parentheses.
3. Simplify the resulting expression.

Q: What is the difference between multiplication and distribution?

A: Multiplication is the process of adding a number a certain number of times, while distribution is the process of multiplying a value outside the parentheses by an expression inside the parentheses.

Q: How do I know when to use the distributive property?

A: You should use the distributive property when you have a multiplication operation inside the parentheses and you want to simplify the expression.

Q: Can I use the distributive property with fractions?

A: Yes, you can use the distributive property with fractions. However, you need to follow the rules of fraction multiplication.

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

A: To simplify an expression with multiple parentheses, follow these steps:

1. Evaluate the innermost parentheses first.
2. Work your way outwards, evaluating each set of parentheses in turn.
3. Simplify the resulting expression.

Q: What are some common mistakes to avoid when using the distributive property?

A: Some common mistakes to avoid when using the distributive property include:

• Forgetting to multiply the value outside the parentheses by each term inside the parentheses.
• Not simplifying the resulting expression.
• Using the distributive property incorrectly with fractions.

Conclusion

In this article, we have covered some of the most frequently asked questions about writing the product of a given expression. We have discussed the order of operations, the distributive property, and how to apply these concepts to simplify expressions. By following these rules and avoiding common mistakes, anyone can become proficient in writing the product of a given expression.

Additional Resources

• For more information on the order of operations, visit www.mathway.com.
• For more information on the distributive property, visit www.khanacademy.org.
• For practice problems and exercises, visit www.mathopenref.com.

Final Thoughts

Writing the product of a given expression is a fundamental skill in algebra that requires a clear understanding of the order of operations and the distributive property. By following these rules and practicing with exercises, anyone can become proficient in simplifying expressions and arriving at the final product.