Match Each Expression To Its Simplified Form By Dragging The Ties To The Correct Boxes To Complete The Pairs.1. $(6r + 7) + (18 + 75) \rightarrow$ $\square$2. $13r + 20 \rightarrow$ $\square$3. $-12 + R

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will explore how to simplify algebraic expressions by combining like terms and applying the order of operations. We will also provide a set of exercises to help you practice and reinforce your understanding of this concept.

What are Algebraic Expressions?

An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Variables are represented by letters, such as x or r, while constants are numbers. Algebraic expressions can be simple, like 2x, or complex, like 2x + 3y - 4.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms and applying the order of operations. Like terms are terms that have the same variable raised to the same power. For example, 2x and 3x are like terms, while 2x and 3y are not.

Combining Like Terms

To combine like terms, we add or subtract the coefficients of the terms. The coefficient is the number that is multiplied by the variable. For example, in the expression 2x + 3x, the coefficients are 2 and 3. We can combine these terms by adding their coefficients:

2x + 3x = (2 + 3)x = 5x

Applying the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when simplifying an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any 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 Given Expressions

Now that we have covered the basics of simplifying algebraic expressions, let's apply what we have learned to the given expressions.

Expression 1: $(6r + 7) + (18 + 75)$

To simplify this expression, we need to combine the like terms and apply the order of operations.

$(6r + 7) + (18 + 75)$

First, we evaluate the expressions inside the parentheses:

$(6r + 7) = 6r + 7$ $(18 + 75) = 93$

Now, we can combine the like terms:

$6r + 7 + 93$

Next, we apply the order of operations:

$6r + 100$

Therefore, the simplified form of the expression is:

$6r + 100$

Expression 2: $13r + 20$

To simplify this expression, we need to combine the like terms and apply the order of operations.

$13r + 20$

This expression is already simplified, so we can move on to the next one.

Expression 3: $-12 + r$

To simplify this expression, we need to combine the like terms and apply the order of operations.

$-12 + r$

This expression is already simplified, so we can move on to the next one.

Conclusion

Simplifying algebraic expressions is a crucial skill to master in mathematics. By combining like terms and applying the order of operations, we can simplify complex expressions and make them easier to work with. In this article, we have covered the basics of simplifying algebraic expressions and applied what we have learned to a set of exercises. We hope that this article has been helpful in reinforcing your understanding of this concept.

Exercises

Now that we have covered the basics of simplifying algebraic expressions, let's practice what we have learned with a set of exercises.

Exercise 1

Simplify the expression: $(3x + 2) + (5x - 3)$

Exercise 2

Simplify the expression: $2x + 5 + 3x - 2$

Exercise 3

Simplify the expression: $-4 + 2x + 3x - 1$

Exercise 4

Simplify the expression: $(2x + 3) + (x - 2)$

Exercise 5

Simplify the expression: $3x + 2 + 2x - 1$

Answer Key

Exercise 1

$(3x + 2) + (5x - 3) = 8x - 1$

Exercise 2

$2x + 5 + 3x - 2 = 5x + 3$

Exercise 3

$-4 + 2x + 3x - 1 = 5x - 5$

Exercise 4

$(2x + 3) + (x - 2) = 3x + 1$

Exercise 5

$3x + 2 + 2x - 1 = 5x + 1$

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 simplifying an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I combine like terms?

A: To combine like terms, we add or subtract the coefficients of the terms. The coefficient is the number that is multiplied by the variable. For example, in the expression 2x + 3x, the coefficients are 2 and 3. We can combine these terms by adding their coefficients:

2x + 3x = (2 + 3)x = 5x

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 number that does not change.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, we need to evaluate the expression inside the parentheses first. Then, we can combine like terms and apply the order of operations.

Q: Can I simplify an expression with multiple variables?

A: Yes, you can simplify an expression with multiple variables. To do this, you need to combine like terms and apply the order of operations.

Q: What is the purpose of simplifying algebraic expressions?

A: The purpose of simplifying algebraic expressions is to make them easier to work with and to make it easier to solve equations and inequalities.

Q: How do I know when an expression is simplified?

A: An expression is simplified when there are no like terms left to combine and the order of operations has been applied.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions. To do this, you need to combine like terms and apply the order of operations.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you need to apply the order of operations and combine like terms.

Q: What is the difference between a simplified expression and a factored expression?

A: A simplified expression is an expression that has been combined and the order of operations has been applied. A factored expression is an expression that has been broken down into its simplest form using factoring techniques.

Q: Can I simplify an expression with negative numbers?

A: Yes, you can simplify an expression with negative numbers. To do this, you need to combine like terms and apply the order of operations.

Q: How do I simplify an expression with decimals?

A: To simplify an expression with decimals, you need to combine like terms and apply the order of operations.

Conclusion

Simplifying algebraic expressions is a crucial skill to master in mathematics. By understanding the order of operations, combining like terms, and applying the rules of algebra, you can simplify complex expressions and make them easier to work with. We hope that this article has been helpful in answering your questions and providing you with a better understanding of simplifying algebraic expressions.