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Order of Operations
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If we hav= e two $5 bill-and two $10-bills,
Order of Operations
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars. 
Order of Operations
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
Order of Operations
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20. 
Order of Operations
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills,
Order of Operations
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars.
Order of Operations
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars. 
In this case, we group= the 3 + 4 in the “(   )” = to indicate that we are to add them first,
Order of Operations
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars. 
In this case, we group= the 3 + 4 in the “(   )” = to indicate that we are to add them first, then multiply the sum to 10 .
Order of Operations
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars. 
In this case, we group= the 3 + 4 in the “(   )” = to indicate that we are to add them first, then multiply the sum to 10 .
Order of Operations
These motivate us to set = the rules for the order of operations.
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars. 
In this case, we group= the 3 + 4 in the “(   )” = to indicate that we are to add them first, then multiply the sum to 10 .
Order of Operations
Order of Operations (excluding taking power)<= /span>
These motivate us to set = the rules for the order of operations.
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars. 
In this case, we group= the 3 + 4 in the “(   )” = to indicate that we are to add them first, then multiply the sum to 10 .
Order of Operations
Order of Operations (excluding taking power)<= /span>
Given an arithmetic expression,= we perform the operations in the following order .
These motivate us to set = the rules for the order of operations.
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars. 
In this case, we group= the 3 + 4 in the “(   )” = to indicate that we are to add them first, then multiply the sum to 10 .
Order of Operations
Order of Operations (excluding taking power)<= /span>
Given an arithmetic expression,= we perform the operations in the following order .
1st .  Do the operations inside of group= ing symbols, starting with the inner most grouping symbol.
These motivate us to set = the rules for the order of operations.
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars. 
In this case, we group= the 3 + 4 in the “(   )” = to indicate that we are to add them first, then multiply the sum to 10 .
Order of Operations
Order of Operations (excluding taking power)<= /span>
Given an arithmetic expression,= we perform the operations in the following order .
1st .  Do the operations inside of group= ing symbols, starting with the inner most grouping symbol.
2nd.  Do multiplications and divisions = (from left to right).
These motivate us to set = the rules for the order of operations.
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If we have two $5 bill= -and two $10-bills, we have the total of 
2(5) + 2(10) =3D 30 dollars.  To get the correct = answer 30,
we multiply the 2 and = the 5 and multiply the 2 and the10 first,
then we add the produc= ts 10 and 20.  =
If I have three $10-bi= lls and you have four $10-bills, we have
3 + 4 =3D 7 $10-bills,= and we’ve in total of (3 + 4)10 =3D 70 dollars. 
In this case, we group= the 3 + 4 in the “(   )” = to indicate that we are to add them first, then multiply the sum to 10 .
Order of Operations
Order of Operations (excluding taking power)<= /span>
Given an arithmetic expression,= we perform the operations in the following order .
1st .  Do the operations inside of group= ing symbols, starting with the inner most grouping symbol.
2nd.  Do multiplications and divisions = (from left to right).
3rd.  Do additions and subtractions (fr= om left to right).
These motivate us to set = the rules for the order of operations.
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Example A.&= #13;
  
= a.  4(–8) + 3(5) =
Order of Operations
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Example A.&= #13;
  
= a.  4(–8) + 3(5) =
Order of Operations
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
Order of Operations
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
Order of Operations
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
Order of Operations
b.   4 + 3(5 + 2)
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
Order of Operations
b.   4 + 3(5 + 2)
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
   =3D 9 – 2[7 – 3= (7)]
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
   =3D 9 – 2[7 – 3= (7)]
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
   =3D 9 – 2[7 – 3= (7)]
   =3D 9 – 2[7 – 2= 1]
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
   =3D 9 – 2[7 – 3= (7)]
   =3D 9 – 2[7 – 2= 1]
   =3D 9 – 2[ –14 ]
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
   =3D 9 – 2[7 – 3= (7)]
   =3D 9 – 2[7 – 2= 1]
   =3D 9 – 2[ –14 ] <= /span>
   =3D 9 + 28
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
   =3D 9 – 2[7 – 3= (7)]
   =3D 9 – 2[7 – 2= 1]
   =3D 9 – 2[ –14 ] <= /span>
   =3D 9 + 28
   =3D 37
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Example A.&= #13;
  
= a.  4(–8) + 3(5) 
   =3D  –32  + 15
   =3D  –17
c.   9 – 2[7 – 3(6 += 1)]
   =3D 9 – 2[7 – 3= (7)]
   =3D 9 – 2[7 – 2= 1]
   =3D 9 – 2[ –14 ] <= /span>
   =3D 9 + 28
   =3D 37
(Don’t perform “4 + 3” or “9 – 2” in the above problems!!)
Order of Operations
b.   4 + 3(5 + 2)
   =3D 4 + 3(7)
   =3D 4 + 21
   =3D 25
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself. 
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself.  N is called the exponent, or the power
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself.  N is called the exponent, or the power = of x, and x is called the= base.
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself.  N is called the exponent, or the power = of x, and x is called the= base.
The base is the quantity immediately beneath the exponent, &#= 13;
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself.  N is called the exponent, or the power = of x, and x is called the= base.
The base is the quantity immediately beneath the exponent,  <= /span>hence 2b3 means 2*b3
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself.  N is called the exponent, or the power = of x, and x is called the= base.
The base is the quantity immediately beneath the exponent,  <= /span>hence 2b3 means 2*b3  =3D 2*b*b*b.
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself.  N is called the exponent, or the power = of x, and x is called the= base.
The base is the quantity immediately beneath the exponent,  <= /span>hence 2b3 means 2*b3  =3D 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third power,
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself.  N is called the exponent, or the power = of x, and x is called the= base.
The base is the quantity immediately beneath the exponent,  <= /span>hence 2b3 means 2*b3  =3D 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third power, we write it as (2b)3
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Exercise: Don’t = do the part that you shouldn’t do!
<= span style=3D'font-size:133%'>1. 6 + 3(3 + 1)        = ;            &n= bsp;     2.  10 – 4(2 = 211; 4)      &nb= sp;
3.  5 + 2[3 + 2(1 + 2)]        = ;        4.   5 – 2[= 3 + 2(5 – 9)]
Order of Operations
Ans: a. 18         b. 18        = ;   c. 23     = ;        4.   15
Exponents
We write x*x*x…*x as xN where N is the number of copies of= x’s multiplied to itself.  N is called the exponent, or the power = of x, and x is called the= base.
The base is the quantity immediately beneath the exponent,  <= /span>hence 2b3 means 2*b3  =3D 2*b*b*b.
If we want multiply 2b to itself three times, i.e. 2b to the third power, we write it as (2b)3 which is (2b)*(2b= )*(2b) =3D8b3. <= /span>
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Order of Operations
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
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Order of Operations
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3). =
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Order of Operations
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3).
    Hence (–3)2 = is (–3)(–3)
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Order of Operations
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3).
    Hence (–3)2 = is (–3)(–3) =3D 9
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Order of Operations
b. Expand – 32
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3).
    Hence (–3)2 = is (–3)(–3) =3D 9
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Order of Operations
b. Expand – 32
    The base of the 2nd power is 3.
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3).
    Hence (–3)2 = is (–3)(–3) =3D 9
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Order of Operations
b. Expand – 32
    The base of the 2nd power is 3.
    Hence – 32  means – (3*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>3)
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3).
    Hence (–3)2 = is (–3)(–3) =3D 9
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Order of Operations
b. Expand – 32
    The base of the 2nd power is 3.
    Hence – 32  means – (3*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>3) =3D – 9
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3).
    Hence (–3)2 = is (–3)(–3) =3D 9
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c. Expand (= 3*2)2 and simplify the answer.
Order of Operations
b. Expand – 32
    The base of the 2nd power is 3.
    Hence – 32  means – (3*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>3) =3D – 9
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3).
    Hence (–3)2 = is (–3)(–3) =3D 9
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c. Expand (= 3*2)2 and simplify the answer.
    The base for the 2nd power is (3*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>2).
Order of Operations
b. Expand – 32
    The base of the 2nd power is 3.
    Hence – 32  means – (3*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>3) =3D – 9
Example B.  (Exponential Notations)
 
a. Expand (–3)2 and simplify the answer.
    The base is (<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>–3).
    Hence (–3)2 = is (–3)(–3) =3D 9
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c. Expand (= 3*2)2 and simplify the answer.
    The base for the 2nd power is (3*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>2).
    Hence(3*2)2