Juan.gutierrez3 at 19:13, 27 September 2021

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Juan.gutierrez3: Created page with "{{{{BOOKTEMPLATE}}/Page}} {{navigation|Book=Algebra |current=Order of Operations |previous=Arithmetic |next=Real_Numbers }} The '''''Order of Operation..."

2021-09-27T19:09:19Z

Created page with "{{{{BOOKTEMPLATE}}/Page}} <noinclude>{{navigation|Book=Algebra |current=Order of Operations |previous=Arithmetic |next=Real_Numbers }}</noinclude> The '''''Order of Operation..."

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<noinclude>{{navigation|Book=Algebra
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|next=Real_Numbers
}}</noinclude>

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.

Example: When faced with <math>4+2 \times 3</math>, how do you proceed?

There are two ways:

<math>4 + 2 \times 3 = (4 + 2) \times 3</math>

<math>4 + 2 \times 3 = 6 \times 3</math>

<math>4 + 2 \times 3= 18</math>

'''or'''

<math>4 + 2 \times 3 = 4 + (2 \times 3)</math>

<math>4 + 2 \times 3 = 4 + 6</math>

<math>4 + 2 \times 3 = 10</math>

This is confusing, so which is correct? (Parentheses, "(" and ")" are used to show what to do first)

In order to communicate using mathematical expressions we must agree on an ''order of operations'' so that each expression has only one value.

For the above example all mathematicians agree the correct answer is 10.

You're probably wondering what this order is.

==The Standard Order of Operations==

Evaluate expressions in this order.

*Parentheses or Brackets (evaluate what's inside them)
*Exponents
*Multiplication and/or division from left to right
*Addition and/or subtraction from left to right

===An Easy Way of Remembering===
Use this memory tool to help remember the order!
'''P'''lease '''E'''xcuse '''M'''y '''D'''ear '''A'''nnoying '''S'''ister
It is also commonly called by its acronym, PEMDAS.

An alternative form of this is;
'''B'''rackets
'''I'''ndices
'''D'''ivision or '''M'''ultiplication
'''A'''ddition or '''S'''ubtraction
(BIDMAS).

Yet another way of remembering this is
'''B'''rackets
'''O'''rders
'''D'''ivision
'''M'''ultiplication
'''A'''ddition
'''S'''ubtraction (BODMAS) 

or '''B'''ring '''O'''ur '''D'''ear '''M'''other '''A'''long '''S'''aturday

==Examples==
{| border="1" cellpadding="5" cellspacing="0"
|+ style="background-color:#cedff2;border:1px solid black;" | '''Order of Operations - Examples'''
|- style="background:#ffdead;"
! Expression
! Evaluation
! Operation
|-
| rowspan="3" | 4 × 2 + 1
| = '''4 × 2''' + 1
| Multiplication
|-
| = '''8 + 1'''
| Addition
|-
| = '''9'''
|
|-
| rowspan="3" | 12 - 9 ÷ 3
| = 12 - '''9 ÷ 3'''
| Division
|-
| = '''12 - 3'''
| Subtraction
|-
| = '''9'''
|
|-
| rowspan="3" | 2 × 9 ÷ 3
| = '''2 × 9''' ÷ 3
| Left to Right
|-
| = '''18 ÷ 3'''
| division
|-
| = '''6'''
|
|-
| rowspan="3" | 9 ÷ 3 × 3
| = ''' 9 ÷ 3''' × 3
| Left to Right
|-
| = '''3 ×3'''
| multiplication
|-
| = '''9'''
|
|-
| rowspan="4" | 3 + 12 ÷ (5 - 2)
| = 3 + 12 ÷ '''(5 - 2)'''
| Parentheses
|-
| = 3 + '''12 ÷ 3'''
| Division
|-
| = '''3 + 4'''
| Addition
|-
| = '''7'''
|
|-
| rowspan="5" | 7 × 10 - (2 × 4)2
| = 7 × 10 - '''(2 × 4)'''2
| Parentheses
|-
| = 7 × 10 - '''82'''
| Exponents
|-
| = '''7 × 10''' - 64
| Multiplication
|-
| = '''70 - 64'''
| Subtraction
|-
| = '''6'''
|
|}

----

== Practice Problems ==
'''Note:''' the expressions in the following quiz, use an asterisk (*) to indicate multiplication (<math>\times</math>) between adjacent factors. This use of the asterisk is nearly ubiquitous with the various computer languages, as the ''times'' symbol is not an historically available keyboard character. Hand written expressions commonly use a small vertically centered dot (·) to indicate multiplication. Where unambiguous, multiplication is ''implied'' between factors and a symbol is extraneous.
<quiz display=simple points="1/1">

{Evaluate the numerical expression
|type="{}"}
<math>2+4*3=</math>{ 14_2 }

{Evaluate the numerical expression
|type="{}"}
<math>2*4+3=</math>{ 11_2 }

{Evaluate the numerical expression
|type="{}"}
<math>(2+4)*3=</math>{ 18_2 }

{Evaluate the numerical expression
|type="{}"}
<math>9^2 + 1 -7*(8+4)/2=</math>{ 40_2 }
</quiz>

== Playing with Mathematics ==

To get yourself thinking about this, try this simple mathematical game:

Take the numbers 1 through 10 on the left side of an equation, and pick a number for the right side.

Example:
1 2 3 4 5 6 7 8 9 10 = 1

Now put operators between those numbers. Only use parentheses when necessary.

Example:
1 + 2 - 3 + 4 - 5 + 6 + 7 + 8 - 9 - 10 = 1

Change the number on the right-hand side. Can you generate an expression for this number? If not, can you prove why not?

Does this change if you change the order of the numbers?

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	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.

Test - Revision history

Juan.gutierrez3 at 19:13, 27 September 2021

Juan.gutierrez3: Created page with "{{{{BOOKTEMPLATE}}/Page}} {{navigation|Book=Algebra |current=Order of Operations |previous=Arithmetic |next=Real_Numbers }} The '''''Order of Operation..."