# Order of Arithmetic Operations: PEMDAS

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

- ๐ There are different orders of operations in math, which can lead to different answers for the same expression
- ๐ Without a defined order, math becomes ambiguous. So a convention called PEMDAS defines the order.
- ๐ PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
- ๐ข Do operations inside Parentheses first, then Exponents, then Multiplication & Division, then Addition & Subtraction.
- ๐ก Apply PEMDAS from left to right when solving math expressions with multiple operations.
- ๐งฎ Following PEMDAS ensures everyone gets the same answer and math remains unambiguous.
- โ๏ธ The order matters - going left to right versus right to left yields different results in expressions.
- โบ๏ธ Parenthetical terms imply grouping; solve inside Parentheses first before continuing expression.
- โ ๏ธ Multiplication and Division happen before Addition and Subtraction in PEMDAS.
- ๐ 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

##### ๐ 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.

##### ๐ 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

##### ๐กArithmetic Operations

##### ๐กOrder of Operations

##### ๐กPEMDAS

##### ๐กMultiplication

##### ๐กDivision

##### ๐กParentheses

##### ๐กExponents

##### ๐กAddition

##### ๐กSubtraction

##### ๐กConsistency in Mathematics

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###### Transcripts

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