1. Simplify: $a \cdot 6 \cdot 4 \div B \quad (b=3$\]2. Simplify: $7 \cdot 2 \div 22 \quad (7=2$\]3. Evaluate: $x - (y - 5), \quad Y=5, \quad X=6$

In mathematics, simplifying algebraic expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will explore three different scenarios where we need to simplify algebraic expressions. We will use the order of operations (PEMDAS) to simplify the expressions and provide step-by-step solutions.

Scenario 1: Simplifying a Multiplication and Division Expression

Problem

Simplify the expression: $a \cdot 6 \cdot 4 \div b \quad (b=3)$

Solution

To simplify this expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers together, and then we will divide the result by $b$.

$a \cdot 6 \cdot 4 \div b = a \cdot (6 \cdot 4) \div b$

Now, we will multiply $6$ and $4$ together.

$a \cdot (6 \cdot 4) \div b = a \cdot 24 \div b$

Next, we will divide $24$ by $b$.

$a \cdot 24 \div b = \frac{a \cdot 24}{b}$

Since we are given that $b=3$, we can substitute this value into the expression.

$\frac{a \cdot 24}{b} = \frac{a \cdot 24}{3}$

Now, we can simplify the expression by dividing $24$ by $3$.

$\frac{a \cdot 24}{3} = 8a$

Therefore, the simplified expression is $8a$.

Scenario 2: Simplifying a Multiplication and Division Expression

Problem

Simplify the expression: $7 \cdot 2 \div 22 \quad (7=2)$

Solution

To simplify this expression, we need to follow the order of operations (PEMDAS). First, we will multiply the numbers together, and then we will divide the result by $22$.

$7 \cdot 2 \div 22 = (7 \cdot 2) \div 22$

Now, we will multiply $7$ and $2$ together.

$(7 \cdot 2) \div 22 = 14 \div 22$

Next, we will divide $14$ by $22$.

$14 \div 22 = \frac{14}{22}$

Now, we can simplify the expression by dividing both the numerator and the denominator by their greatest common divisor, which is $2$.

$\frac{14}{22} = \frac{7}{11}$

Therefore, the simplified expression is $\frac{7}{11}$.

Scenario 3: Evaluating an Expression with Parentheses

Problem

Evaluate the expression: $x - (y - 5), \quad y=5, \quad x=6$

Solution

To evaluate this expression, we need to follow the order of operations (PEMDAS). First, we will evaluate the expression inside the parentheses.

$y - 5 = 5 - 5 = 0$

Now, we will substitute this value back into the original expression.

$x - (y - 5) = x - 0$

Next, we will substitute the value of $x$ into the expression.

$x - 0 = 6 - 0 = 6$

Therefore, the value of the expression is $6$.

Conclusion

In this article, we have explored three different scenarios where we need to simplify algebraic expressions. We have used the order of operations (PEMDAS) to simplify the expressions and provide step-by-step solutions. By following the order of operations, we can simplify complex expressions and arrive at the correct solution.

Tips and Tricks

• Always follow the order of operations (PEMDAS) when simplifying algebraic expressions.
• Use parentheses to group numbers and variables together.
• Simplify expressions by combining like terms.
• Use the greatest common divisor to simplify fractions.

Practice Problems

1. Simplify the expression: $3 \cdot 2 \div 6 \quad (3=2)$
2. Evaluate the expression: $x + (y + 5), \quad y=3, \quad x=4$
3. Simplify the expression: $a \cdot 5 \cdot 3 \div b \quad (b=2)$

Answer Key

1. $\frac{1}{2}$
2. $7$
3. $15a$
   Frequently Asked Questions: Simplifying Algebraic Expressions ===========================================================

In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions. Whether you are a student or a teacher, these questions and answers will help you understand the concepts and techniques involved in simplifying algebraic expressions.

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying algebraic expressions. The acronym PEMDAS stands for:

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

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to follow the order of operations (PEMDAS). First, evaluate any expressions inside the parentheses. Then, simplify the expression by combining like terms.

For example, consider the expression: $x - (y - 5)$

To simplify this expression, we need to evaluate the expression inside the parentheses first.

$y - 5 = 5 - 5 = 0$

Now, we can substitute this value back into the original expression.

$x - (y - 5) = x - 0$

Next, we can simplify the expression by combining like terms.

$x - 0 = x$

Therefore, the simplified expression is $x$.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you need to follow the order of operations (PEMDAS). First, evaluate any exponential expressions. Then, simplify the expression by combining like terms.

For example, consider the expression: $2^3 \cdot 3^2$

To simplify this expression, we need to evaluate the exponential expressions first.

$2^3 = 8$

$3^2 = 9$

Now, we can substitute these values back into the original expression.

$2^3 \cdot 3^2 = 8 \cdot 9$

Next, we can simplify the expression by combining like terms.

$8 \cdot 9 = 72$

Therefore, the simplified expression is $72$.

Q: How do I simplify an expression with fractions?

A: To simplify an expression with fractions, you need to follow the order of operations (PEMDAS). First, simplify any fractions by dividing both the numerator and the denominator by their greatest common divisor. Then, simplify the expression by combining like terms.

For example, consider the expression: $\frac{14}{22}$

To simplify this expression, we need to divide both the numerator and the denominator by their greatest common divisor, which is $2$.

$\frac{14}{22} = \frac{7}{11}$

Therefore, the simplified expression is $\frac{7}{11}$.

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, consider the expression: $x + 5$

In this expression, $x$ is a variable because its value can change. The value $5$ is a constant because it 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 order of operations (PEMDAS). First, simplify any fractions by dividing both the numerator and the denominator by their greatest common divisor. Then, simplify the expression by combining like terms.

For example, consider the expression: $x + 5$

To simplify this expression, we need to combine the variable and the constant.

$x + 5 = x + 5$

Therefore, the simplified expression is $x + 5$.

Conclusion

In this article, we have answered some of the most frequently asked questions about simplifying algebraic expressions. We have covered topics such as the order of operations (PEMDAS), simplifying expressions with parentheses, exponents, and fractions, and the difference between variables and constants. By following the order of operations and simplifying expressions, you can arrive at the correct solution and understand the concepts and techniques involved in simplifying algebraic expressions.

Practice Problems

1. Simplify the expression: $3 \cdot 2 \div 6 \quad (3=2)$
2. Evaluate the expression: $x + (y + 5), \quad y=3, \quad x=4$
3. Simplify the expression: $a \cdot 5 \cdot 3 \div b \quad (b=2)$

Answer Key

1. $\frac{1}{2}$
2. $7$
3. $15a$