Order of Arithmetic Operations: PEMDAS

Professor Dave Explains
19 Aug 201704:21
EducationalLearning
32 Likes 10 Comments

TLDRThe video explains the proper order of operations for arithmetic expressions. It starts with an example that shows how starting from different sides gives different answers. This demonstrates the need for an agreed upon convention - PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. This is the order operations should be performed in an expression, from left to right. Following this order ensures everyone gets the same result. The video then walks through some examples, showing how to apply PEMDAS to get the correct evaluation of complex expressions.

Takeaways
  • 😀 There are different orders of operations in math, which can lead to different answers for the same expression
  • 😟 Without a defined order, math becomes ambiguous. So a convention called PEMDAS defines the order.
  • 📒 PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
  • 🔢 Do operations inside Parentheses first, then Exponents, then Multiplication & Division, then Addition & Subtraction.
  • 💡 Apply PEMDAS from left to right when solving math expressions with multiple operations.
  • 🧮 Following PEMDAS ensures everyone gets the same answer and math remains unambiguous.
  • ✏️ The order matters - going left to right versus right to left yields different results in expressions.
  • ⏺️ Parenthetical terms imply grouping; solve inside Parentheses first before continuing expression.
  • ⚠️ Multiplication and Division happen before Addition and Subtraction in PEMDAS.
  • 🎓 Check comprehension by evaluating complex expressions on your own using proper PEMDAS order.
Q & A

  • What does PEMDAS stand for?

    -PEMDAS is an acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It represents the conventional order of operations that allows everyone to get the same answer when evaluating mathematical expressions.

  • Why do we need an order of operations like PEMDAS?

    -We need an order of operations like PEMDAS because otherwise the order in which operations are performed is ambiguous, and people could get different answers for the same expression. PEMDAS provides a standardized convention.

  • What operation takes precedence in PEMDAS?

    -The operations inside parentheses take precedence over all other operations in PEMDAS. After parentheses, exponents take precedence, followed by multiplication and division, and finally addition and subtraction.

  • In the expression 5 * 3 + 4 - 2 * 6, what is the result if we evaluate from left to right?

    -If we evaluate the expression from left to right, we get: 5 * 3 = 15, 15 + 4 = 19, 19 - 2 = 17, 17 * 6 = 102.

  • In the same expression, what do we get if we evaluate from right to left?

    -If we evaluate from right to left, we get: 2 * 6 = 12, 4 - 12 = -8, 3 + -8 = -5, 5 * -5 = -25. This is incorrect based on PEMDAS.

  • How do we handle exponents in PEMDAS?

    -Exponents come after parentheses but before multiplication/division in PEMDAS. So we would simplify all exponential terms before applying multiplication or division.

  • In the expression 15 + 3 + 2^2 - 9 * 6 + 2^3, what is the first step based on PEMDAS?

    -The first step based on PEMDAS is to evaluate the parenthetical expression 2^2. We simplify 2^2 to get 4.

  • After applying PEMDAS to 15 + 3 + 2^2 - 9 * 6 + 2^3, what is the result?

    -After fully applying PEMDAS, we get: 15 + 3 + 4 - 54 + 8 = -6.

  • Does PEMDAS specify if you go from left to right or right to left when doing addition/subtraction or multiplication/division?

    -PEMDAS does not specify. You can go left to right or right to left when doing addition/subtraction or multiplication/division. The key is to perform all of one operation before moving to the next in the hierarchy.

  • If an expression has multiple sets of parentheses, which do you evaluate first?

    -If there are multiple sets of parentheses, you evaluate the innermost parentheses first, then work your way outwards following PEMDAS order.

Outlines
00:00
😃 Introducing Order of Operations (PEMDAS)

The paragraph introduces the concept of order of operations, known as PEMDAS - Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. It explains why order of operations is important when evaluating expressions with multiple operations to ensure everyone gets the same answer. Examples are provided to illustrate the application of PEMDAS.

😀 Checking Comprehension on Using Order of Operations

The paragraph encourages checking your own comprehension on properly applying order of operations (PEMDAS) when evaluating mathematical expressions. This allows confirming you can evaluate expressions correctly following the established convention.

Mindmap
Keywords
💡Arithmetic Operations
Arithmetic operations include basic mathematical processes such as addition, subtraction, multiplication, division, and exponentiation. These operations form the foundation of algebra and are crucial for performing calculations. In the context of the video, the discussion begins by listing these operations to set the stage for understanding how they interact when multiple operations are applied within a single expression. The video emphasizes the importance of knowing the order in which these operations should be executed to achieve a correct and consistent result.
💡Order of Operations
The Order of Operations is a set of rules that specifies the sequence in which multiple arithmetic operations should be performed within a mathematical expression to ensure a single, correct outcome. The video introduces PEMDAS, an acronym that stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right), as the convention followed to resolve expressions with multiple operations. This concept is central to the video's theme, highlighting the necessity of a standardized approach to avoid ambiguity and inconsistency in mathematical calculations.
💡PEMDAS
PEMDAS is an acronym used to remember the correct order of operations in mathematics: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. This rule guides the sequence of operations to ensure consistent results across different calculations. The video uses PEMDAS to demonstrate how to correctly solve complex expressions by applying operations in their proper order, emphasizing its role in achieving uniformity and accuracy in mathematics.
💡Multiplication
Multiplication, one of the basic arithmetic operations, involves combining equal groups to find a total number. It is symbolized by the 'times' sign (×). In the video, multiplication is discussed as a priority operation according to the PEMDAS rule, where it should be performed before addition and subtraction in the absence of parentheses or exponents. Examples from the script illustrate this by solving parts of expressions using multiplication before moving on to addition or subtraction.
💡Division
Division is an arithmetic operation that involves splitting a number into equal parts or groups. It is the inverse of multiplication. In the context of PEMDAS, division is treated with the same priority as multiplication and should be performed right after multiplication (or simultaneously, respecting the left-to-right rule for operations of the same rank). The video script implies this rule but focuses more on multiplication and addition examples to demonstrate the order of operations.
💡Parentheses
Parentheses are symbols used in mathematics to group parts of an expression, indicating that the operations enclosed should be performed first. This is the 'P' in PEMDAS. The video discusses how operations within parentheses have the highest priority and must be completed before addressing any outside operations. This concept is illustrated with examples where expressions include parenthetical terms, emphasizing their role in altering the standard sequence of operations.
💡Exponents
Exponents, represented by a superscript number next to a base, indicate how many times the base is multiplied by itself. They are the second priority in the PEMDAS rule. The video explains that after solving any operations within parentheses, exponents must be addressed before moving on to multiplication, division, addition, or subtraction. Examples in the script show how exponents change the value of numbers significantly before further operations are applied.
💡Addition
Addition is a basic arithmetic operation that combines two or more numbers to find a sum. It is one of the final steps in the order of operations, performed after parentheses, exponents, multiplication, and division have been resolved. The video uses addition to illustrate how, once the higher-priority operations are completed, the remaining expression can be simplified through addition and subtraction, following the left-to-right rule.
💡Subtraction
Subtraction, the process of removing one number from another to find the difference, is treated with the same priority as addition in the order of operations. The video script includes examples where subtraction is used in the final stages of simplifying an expression, after all higher-priority operations have been executed. This demonstrates subtraction’s role in achieving the final result of a complex mathematical expression.
💡Consistency in Mathematics
The concept of consistency in mathematics refers to the need for uniform methods and rules that ensure the same procedures yield the same results, regardless of who performs them or in what context. The video highlights this principle through the introduction of the order of operations, showing that without a universally accepted method (like PEMDAS) for resolving expressions with multiple operations, various interpretations could lead to differing outcomes. This underscores the importance of standardized conventions in mathematics for maintaining consistency and reliability in calculations.
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Transcripts

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