Order of Operations - Revision history

Lila at 22:58, 15 October 2021

2021-10-15T22:58:40Z

Lila at 22:57, 15 October 2021

2021-10-15T22:57:11Z

Juan.gutierrez3: Added licensing section at the bottom

2021-10-11T14:40:09Z

Added licensing section at the bottom

Juan.gutierrez3: Updated from wikibooks

2021-09-30T14:24:25Z

Updated from wikibooks

Show changes

Lila: /* Resources and Examples */

2021-09-15T15:21:34Z

Resources and Examples

Lila at 18:09, 14 September 2021

2021-09-14T18:09:14Z

Lila at 18:08, 14 September 2021

2021-09-14T18:08:39Z

Lila at 17:53, 14 September 2021

2021-09-14T17:53:47Z

Lila at 17:51, 14 September 2021

2021-09-14T17:51:59Z

Lila: /* Resources and Examples */

2021-09-14T17:46:14Z

Resources and Examples

← Older revision		Revision as of 22:58, 15 October 2021
Line 1:		Line 1:
−	~~<span style="color:#FF33CC"> PINK TEST </span>~~
−
	The '''''Order of Operations''''' is used when doing expressions with more than one operation (e.g., ×, +, -). These are rules so you only get one answer all the time.		The '''''Order of Operations''''' is used when doing expressions with more than one operation (e.g., ×, +, -). These are rules so you only get one answer all the time.

← Older revision		Revision as of 22:57, 15 October 2021
Line 1:		Line 1:
		+	<span style="color:#FF33CC"> PINK TEST </span>
		+
	The '''''Order of Operations''''' is used when doing expressions with more than one operation (e.g., ×, +, -). These are rules so you only get one answer all the time.		The '''''Order of Operations''''' is used when doing expressions with more than one operation (e.g., ×, +, -). These are rules so you only get one answer all the time.

← Older revision		Revision as of 14:40, 11 October 2021
Line 176:		Line 176:

	Does this change if you change the order of the numbers?		Does this change if you change the order of the numbers?
		+
		+
		+	== Licensing ==
		+	Content obtained from [https://en.wikibooks.org/w/index.php?title=Algebra/Order_of_Operations&oldid=3662722 Order of Operations, Algebra, at Wikibooks] under a CC BY-SA license

@@ Line 20: / Line 20: @@
 A common acronym used to memorize the order of operations is "PEMDAS": parentheses, exponents (which includes calculating roots), multiplication and division, and addition and subtraction.
-==Resources and Examples==
+==Resources==
 * [https://en.wikipedia.org/wiki/Order_of_operations Order of Operations], Wikipedia
 * [https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-of-operations/v/introduction-to-order-of-operations Introduction to Order of Operations], Khan Academy
 * [https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-arithmetic-operations/cc-6th-order-of-operations/e/evaluating-numerical-expressions-with-exponents Order of Operations Practice Problems], Khan Academy
 * [https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Support_Course_for_Elementary_Statistics/Operations_on_Numbers/Order_of_Operations Order of Operations], LibreTexts

@@ Line 6: / Line 6: @@
 ==Definition==
-The order of operations, which is used throughout mathematics, science, technology and many computer [[programming language]]s, is expressed here:
+The order of operations, which is used throughout mathematics, science, technology and many computer programming languages, is expressed here:
 # parentheses
 # exponentiation and root extraction
@@ Line 12: / Line 12: @@
 # addition and subtraction
-This means that if, in a mathematical expression, a subexpression appears between two [[Operator (programming)|operators]], the operator that is higher in the above list should be applied first. Expressions in parentheses take precedence over expressions outside of them (for example, (3 + 4) × 7 = 7 × 7 = 49, and not 3 + 4 × 7 = 3 + 28 = 31, despite the fact that multiplication takes precedence over addition). Within a single set of parentheses, the normal order of operations applies.
+This means that if, in a mathematical expression, a subexpression appears between two operators, the operator that is higher in the above list should be applied first. Expressions in parentheses take precedence over expressions outside of them (for example, (3 + 4) × 7 = 7 × 7 = 49, and not 3 + 4 × 7 = 3 + 28 = 31, despite the fact that multiplication takes precedence over addition). Within a single set of parentheses, the normal order of operations applies.
 The commutative property and associative property laws of addition and multiplication allow adding terms in any order, and multiplying factors in any order—but mixed operations must obey the standard order of operations.

@@ Line 5: / Line 5: @@
 These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used to indicate an alternative order of operations (or to simply reinforce the default order of operations). For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5)2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by brackets or braces to avoid confusion, as in [2 × (3 + 4)] − 5 = 9.
-A common acronym used to memorize the order of operations is "PEMDAS": parentheses, exponents, multiplication and division, and addition and subtraction.
+==Definition==
 ==Resources and Examples==

← Older revision		Revision as of 17:53, 14 September 2021
Line 4:		Line 4:

	These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used to indicate an alternative order of operations (or to simply reinforce the default order of operations). For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5)2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by brackets or braces to avoid confusion, as in [2 × (3 + 4)] − 5 = 9.		These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used to indicate an alternative order of operations (or to simply reinforce the default order of operations). For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5)2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by brackets or braces to avoid confusion, as in [2 × (3 + 4)] − 5 = 9.
		+
		+	A common acronym used to memorize the order of operations is "PEMDAS": parentheses, exponents, multiplication and division, and addition and subtraction.

	==Resources and Examples==		==Resources and Examples==

@@ Line 1: / Line 1: @@
 In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression.
-For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation.[1][2] Thus, the expression 1 + 2 × 3 is interpreted to have the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base.[1] Thus 3 + 52 = 28 and 3 × 52 = 75.
+For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, the expression 1 + 2 × 3 is interpreted to have the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base.[1] Thus 3 + 52 = 28 and 3 × 52 = 75.
 These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used to indicate an alternative order of operations (or to simply reinforce the default order of operations). For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5)2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by brackets or braces to avoid confusion, as in [2 × (3 + 4)] − 5 = 9.