Match Each Product To The Equivalent Expression Written As A Sum.1. ${$5(7+3)$}$2. ${$3(9+7)$}$3. ${$7(5+3)$}$4. ${ 3(7+5)\$}

Mar 10, 2025 by ADMIN 126 views

Simplifying Algebraic Expressions: A Guide to Evaluating Products

In mathematics, algebraic expressions are a fundamental concept that helps us represent and solve various mathematical problems. One of the key aspects of algebraic expressions is simplifying them to their most basic form. In this article, we will focus on simplifying products of expressions written as sums. We will explore four different examples and learn how to match each product to its equivalent expression written as a sum.

Understanding the Basics of Algebraic Expressions

Before we dive into the examples, let's quickly review the basics of algebraic expressions. An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be written in various forms, including sums, differences, products, and quotients.

Example 1: Simplifying ${ $5(7+3)\$}$

Let's start with the first example: ${ $5(7+3)\$}$ . To simplify this expression, we need to follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

The expression ${ $5(7+3)\$}$ can be simplified as follows:

Evaluate the expression inside the parentheses: ${ $7+3=10\$}$
Multiply 5 by the result: ${ $5\times10=50\$}$

Therefore, the simplified form of the expression ${ $5(7+3)\$}$ is 50.

Example 2: Simplifying ${ $3(9+7)\$}$

Now, let's move on to the second example: ${ $3(9+7)\$}$ . To simplify this expression, we need to follow the same order of operations as before.

The expression ${ $3(9+7)\$}$ can be simplified as follows:

Evaluate the expression inside the parentheses: ${ $9+7=16\$}$
Multiply 3 by the result: ${ $3\times16=48\$}$

Therefore, the simplified form of the expression ${ $3(9+7)\$}$ is 48.

Example 3: Simplifying ${ $7(5+3)\$}$

Next, let's consider the third example: ${ $7(5+3)\$}$ . To simplify this expression, we need to follow the same order of operations as before.

The expression ${ $7(5+3)\$}$ can be simplified as follows:

Evaluate the expression inside the parentheses: ${ $5+3=8\$}$
Multiply 7 by the result: ${ $7\times8=56\$}$

Therefore, the simplified form of the expression ${ $7(5+3)\$}$ is 56.

Example 4: Simplifying ${ $3(7+5)\$}$

Finally, let's consider the fourth example: ${ $3(7+5)\$}$ . To simplify this expression, we need to follow the same order of operations as before.

The expression ${ $3(7+5)\$}$ can be simplified as follows:

Evaluate the expression inside the parentheses: ${ $7+5=12\$}$
Multiply 3 by the result: ${ $3\times12=36\$}$

Therefore, the simplified form of the expression ${ $3(7+5)\$}$ is 36.

Conclusion

In this article, we have explored four different examples of simplifying products of expressions written as sums. We have learned how to follow the order of operations (PEMDAS) and evaluate expressions inside parentheses before multiplying. By applying these concepts, we have simplified each expression to its most basic form.

Key Takeaways

Algebraic expressions are a fundamental concept in mathematics that helps us represent and solve various mathematical problems.
Simplifying algebraic expressions is an essential skill that helps us evaluate and solve mathematical problems.
To simplify products of expressions written as sums, we need to follow the order of operations (PEMDAS) and evaluate expressions inside parentheses before multiplying.
By applying these concepts, we can simplify complex algebraic expressions and arrive at their most basic form.

Final Thoughts

Simplifying algebraic expressions is a crucial skill that helps us evaluate and solve mathematical problems. By following the order of operations (PEMDAS) and evaluating expressions inside parentheses before multiplying, we can simplify complex algebraic expressions and arrive at their most basic form. Whether you are a student or a professional, mastering the art of simplifying algebraic expressions will help you tackle complex mathematical problems with confidence and ease.
Frequently Asked Questions: Simplifying Algebraic Expressions

In our previous article, we explored the concept of simplifying algebraic expressions, focusing on products of expressions written as sums. We learned how to follow the order of operations (PEMDAS) and evaluate expressions inside parentheses before multiplying. In this article, we will address some of the most frequently asked questions related to simplifying algebraic expressions.

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

A: The order of operations (PEMDAS) is a set of rules that helps us evaluate mathematical expressions in the correct order. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It tells us to:

Evaluate expressions inside parentheses first
Evaluate any exponents (such as squaring or cubing) next
Perform any multiplication and division operations from left to right
Finally, perform any addition and subtraction operations from left to right

Q: Why is it important to follow the order of operations?

A: Following the order of operations is crucial because it ensures that mathematical expressions are evaluated correctly. If we don't follow the order of operations, we may arrive at incorrect answers or even change the meaning of the expression.

Q: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, we need to follow the order of operations (PEMDAS). We start by evaluating expressions inside parentheses, then exponents, and finally any multiplication and division operations from left to right. Finally, we perform any addition and subtraction operations from left to right.

Q: What is the difference between a product and a sum?

A: A product is the result of multiplying two or more numbers together, while a sum is the result of adding two or more numbers together. For example, 3 × 4 is a product, while 3 + 4 is a sum.

Q: How do I simplify expressions with variables?

A: To simplify expressions with variables, we need to follow the same rules as before. We start by evaluating expressions inside parentheses, then exponents, and finally any multiplication and division operations from left to right. Finally, we perform any addition and subtraction operations from left to right.

Q: Can I simplify expressions with fractions?

A: Yes, we can simplify expressions with fractions by following the same rules as before. We start by evaluating expressions inside parentheses, then exponents, and finally any multiplication and division operations from left to right. Finally, we perform any addition and subtraction operations from left to right.

Q: What is the most important thing to remember when simplifying algebraic expressions?

A: The most important thing to remember when simplifying algebraic expressions is to follow the order of operations (PEMDAS). This will ensure that you evaluate expressions correctly and arrive at the correct answer.

Q: Can I use a calculator to simplify algebraic expressions?

A: Yes, you can use a calculator to simplify algebraic expressions. However, it's always a good idea to double-check your work by following the order of operations (PEMDAS) and evaluating expressions manually.

Conclusion

Key Takeaways

The order of operations (PEMDAS) is a set of rules that helps us evaluate mathematical expressions in the correct order.
Following the order of operations is crucial because it ensures that mathematical expressions are evaluated correctly.
To simplify expressions with multiple operations, we need to follow the order of operations (PEMDAS).
A product is the result of multiplying two or more numbers together, while a sum is the result of adding two or more numbers together.
To simplify expressions with variables, we need to follow the same rules as before.
We can simplify expressions with fractions by following the same rules as before.

Final Thoughts