# How To Evaluate Expressions With Variables Using Order of Operations

TLDRThis educational video script delves into the intricacies of evaluating mathematical expressions involving variables, fractions, and exponents. It emphasizes the importance of the order of operations, using the acronym PEMDAS to guide viewers through the correct sequence: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). The script provides step-by-step examples to illustrate how to handle complex expressions and demonstrates the process of evaluating algebraic expressions by substituting given values for variables. It also highlights the impact of operation order on the final result, ensuring viewers understand the fundamental rules of mathematical computation.

###### Takeaways

- ๐ The importance of order of operations is emphasized, with the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) guiding the sequence of mathematical operations.
- ๐ข Multiplication and division are of equal priority and should be performed from left to right when they appear in an expression without parentheses.
- โ Addition and subtraction also have equal priority and are executed from left to right in an expression.
- ๐ Parentheses take precedence over all other operations and should be calculated first.
- ๐ก Exponents represent repeated multiplication and are calculated before multiplication and division.
- ๐ค The script provides examples to illustrate the correct order of operations, emphasizing the difference in outcomes based on the order in which operations are performed.
- ๐ In expressions with variables and exponents, the order of operations must still be followed, with exponents calculated first, followed by multiplication and division, and finally addition and subtraction.
- ๐ The video script includes examples with variables, demonstrating how to substitute values for variables and then perform the operations in the correct order.
- ๐ The process of evaluating algebraic expressions is explained step by step, with a focus on correctly applying the order of operations.
- ๐ The script also covers expressions with fractions, showing how to convert them into multiplication and division for easier calculation.
- ๐ The final examples in the script involve more complex expressions, reinforcing the need to follow the order of operations to arrive at the correct answer.

###### Q & A

### What is the correct order of operations in mathematics?

-The correct order of operations is given by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

### Why does the order of operations matter in evaluating expressions?

-The order of operations matters because it determines the sequence in which calculations are performed, which can lead to different results if not followed correctly.

### What is the result of the expression 7 + 4 * 3 when evaluated using the order of operations?

-Following the order of operations, you first multiply 4 by 3 to get 12, then add 7 to get a result of 19.

### How does the order of operations affect the expression 36 - 12 / 3?

-According to PEMDAS, division has priority over subtraction, so you divide 12 by 3 to get 4, and then subtract that from 36 to get 32.

### What is the result of the expression 24 / 6 * 2 if you perform the operations from left to right?

-When you divide 24 by 6 first, you get 4, and then multiplying that by 2 gives you a result of 8.

### How do you evaluate the expression 8 * 5 / 4?

-You can simply multiply from left to right: 8 times 5 gives 40, and then dividing that by 4 gives a result of 10.

### What is the result of the expression 24 + 12 / 10 - 4?

-First, you add 24 and 12 to get 36, then subtract 4 from 10 to get 6, and finally divide 36 by 6 to get a result of 6.

### How do you evaluate the expression involving the sum and product within parentheses: 4 * (3 + 5) - 7 * 2?

-First, calculate the sum inside the parentheses (3 + 5 = 8), then multiply by 4 to get 32, and subtract the product of 7 and 2 (14) from 32 to get a result of 18.

### What is the result of the complex expression 3 * 4 - 2 * (3^3 - 2^4) + 8 * 2?

-First, calculate the exponents: 3^3 is 27 and 2^4 is 16. Then perform the operations inside the parentheses (27 - 16 = 11), multiply by 2 to get 22, subtract that from 4, and continue with the rest of the expression to get a final result of -38.

### How do you evaluate an algebraic expression with variables like 4x + 2y - 3z given specific values for x, y, and z?

-Substitute the given values for x, y, and z into the expression. For example, if x=2, y=3, and z=-4, you would calculate 4*2 + 2*3 - 3*(-4), which simplifies to 8 + 6 + 12, resulting in 26.

### What is the result of the expression x^2 + 3y^3 / (2z + 1) given x=4, y=2, and z=4.5?

-First, calculate the squares and cubes: x^2 is 16 and y^3 is 8. Then multiply 3 by 8 to get 24. Next, calculate the denominator: 2z + 1 is 2*4.5 + 1, which is 9 + 1. Finally, divide (16 + 24) by 10 to get a result of 4.

### How do you evaluate the expression 4x + y - z / 3 with x=3, y=4, and z=12?

-First, add x and y to get 3 + 4 = 7. Then divide z by 3 to get 12 / 3 = 4. Multiply these results to get 4 * 7 = 28, and subtract the division result to get 28 - 4, resulting in 24.

###### Outlines

##### ๐งฎ Understanding Order of Operations

This paragraph introduces the concept of order of operations, emphasizing the importance of following the correct sequence when performing mathematical calculations. It explains the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) as a guide to remember the hierarchy of operations. The paragraph provides examples to illustrate how the order affects the outcome, such as calculating '7 + 4 * 3' which results in 19, not 33, due to multiplication being performed before addition. It also discusses the equal priority of multiplication and division, and addition and subtraction, and how to proceed when these operations are adjacent.

##### ๐ Advanced Mathematical Expressions with PEMDAS

The second paragraph delves into more complex mathematical expressions involving variables, fractions, and exponents, while still adhering to the order of operations. It demonstrates how to evaluate expressions with parentheses and exponents, such as '3 * 4 - 2 * 3^3 - 2^4 + 8 * 2', by first addressing the exponents and then proceeding with the rest of the operations in the correct order. The paragraph also covers how to handle expressions with variables, like '4x + 2y - 3z', by substituting the given values for x, y, and z before performing the calculations.

##### ๐ข Evaluating Algebraic Expressions with Variables

The final paragraph focuses on evaluating algebraic expressions that include variables and operations. It provides step-by-step instructions on how to substitute values for variables within an expression and then carry out the necessary calculations. Examples given include expressions with squared and cubed terms, as well as division by a variable. The paragraph concludes with a straightforward example of '4x + y - z / 3', where specific values for x, y, and z are substituted to arrive at the final answer, reinforcing the process of evaluating expressions by following the order of operations and performing substitutions.

###### Mindmap

###### Keywords

##### ๐กOrder of Operations

##### ๐กParentheses

##### ๐กExponents

##### ๐กMultiplication

##### ๐กDivision

##### ๐กAddition

##### ๐กSubtraction

##### ๐กVariables

##### ๐กAlgebraic Expression

##### ๐กFractions

###### Highlights

The importance of understanding the order of operations (PEMDAS) in performing mathematical calculations is emphasized, highlighting the need to prioritize operations based on their position in an expression.

The correct order of operations for the expression '7 plus 4 times 3' is multiplication before addition, resulting in 19 instead of 33.

The expression '36 minus 12 divided by 3' demonstrates the priority of division over subtraction, leading to the correct answer of 32.

The concept of PEMDAS is further explained, with multiplication and division having equal priority and addition and subtraction having the same priority, but multiplication and division are performed from left to right.

The expression '24 divided by 6 multiplied by 2' illustrates the importance of the order of operations, with multiplication and division having the same priority, leading to different answers depending on the order.

The example '24 plus 12 divided by 10 minus 4' is used to show that evaluating algebraic expressions involves substituting values and performing the operations from left to right.

The expression 'three multiplied by four minus two times three to the third power minus two to the fourth power plus eight times two' demonstrates the need to work inside parentheses and handle exponents correctly.

The calculation '4x plus 2y, minus 3z' with x=2, y=3, and z=-4 shows how substitution of values into an algebraic expression leads to the correct answer.

The expression 'x squared plus three y cubed divided by two z plus one' with x=4, y=2, and z=4.5 is used to illustrate the process of evaluating expressions with variables, resulting in 9.

The final example '4 times x plus y, minus z divided by 3' with x=3, y=4, and z=12 is used to demonstrate the process of evaluating an expression with variables, leading to the correct answer of 24.

###### Transcripts

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