Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Mathematics 1MPES2
Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Mathematics 1MPES2
Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Mathematics 1MPES2
Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Mathematics 1MPES2

Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Lyc£©e Jean-Piaget - Neuch£¢tel 2015-2016 Mathematics 1MPES2

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  • Lycée Jean-Piaget - Neuchâtel 2015-2016

    Mathematics 1MPES2 Chapter 1

    Order  of  Operations  

    1.  To  simplify  an  expression:   • We proceed in this order:

    1. _____________

    2. _____________

    3. ___________________________

    4. ___________________________

    • To remember:

    • Mnemonic device: ________________________________________

    2.  Examples:   • 5 − 3 2 + 4! =  5 − 3 2 + 16  

    • 5 − 3 2 + 16 = 5 − 3 18  

    • 5 − 3 18 = 5 − 54  

    • 5 − 54 = −49  so  the  result  is:   − 49  

     

    • 30 ÷ 5 2 + 4 − 7 ! = 30 ÷ 5 2 + −3 !

    • 30 ÷ 5 2 + −3 ! = 30 ÷ 5 2 + 9

    • 30 ÷ 5 2 + 9 = 6 2 + 9

    • 6 2 + 9 = 12 + 9

    • 12 + 9 = 21 so the result is 21  

  • Lycée Jean-Piaget - Neuchâtel 2015-2016

    Mathematics 1MPES2 Chapter 1

    3.  Practical  exercises:   • 4 + 3 4 − 2 = 4 + 3 2

    • 4 + 3 2 = 4 + 6

    • 4 + 6 = 10  so  the  result  is:  10

     

    • 12 ÷ 2 + 3 − 8 != 12 ÷ 2 + −5 !

    • 12 ÷ 2 + −5 ! = 12 ÷ 2 + 25

    • 12 ÷ 2 + 25 = 6 + 25

    • 6 + 25 = 31  so  the  result  is:  31

    4.  Different  types  of  parenthesis:    

    • Always do _________________ first !

    5.  Examples:   • 4 + 2 − 5! ÷ 2 + 3 = 4 + 2 − 5! ÷ 5

    • 4 + 2 − 5! ÷ 5 = 4 + 2 − 25 ÷ 5

    • 4 + 2 − 5 = 6 − 5

    • 6 − 5 = 1  so  the  result  is:  1

     

    • 7 2! + 2 20 ÷ 4 + 6 = 7 2! + 2 20 ÷ 10

    • 7 2! + 2 20 ÷ 10 = 7 2! + 2 2

    • 7 2! + 2 2 = 7 2! + 4

    • 7 2! + 4 = 7 4 + 4

    • 7 4 + 4 = 7 8

    • 7 8 = 56  so  the  result  is:  56

  • Lycée Jean-Piaget - Neuchâtel 2015-2016

    Mathematics 1MPES2 Chapter 1

    6.  Practical  exercises:   • 3 8 + 2 8 ∙ 6 − 29 = 3 8 + 2 48 − 29

    • 3 8 + 2 48 − 29 = 3 8 + 2 19

    • 3 8 + 2 19 = 3 8 + 38

    • 3 8 + 38 = 3 46

    • 3 46 = 138  so  the  result  is:  138

     

    • 9 − 16 ! ∙ 9! ÷ 1 + 8 = 9 − 16 ! ∙ 9! ÷ 9

    • 9 − 16 ! ∙ 729 ÷ 9 = 9 − 16 ! ∙ 81

    • −7 ! ∙ 81 = 49 ∙ 81

    • 49 ∙ 81 = 3!969  so  the  result  is:  3!969

    7.  Simplify  fractions  with  parenthesis:    

    • When simplifying fractions, always simplify

    ____ and __________ first !

    • Then ________________.

    8.  Examples:  

    • !!!! !!!∙! !!! !!!

    =

    Top   Bottom  

    −4! − 4 + 2 ∙ 3 = −4! − 4 + 6  

    −4! − 4 + 6 = −4! − 10  

    −4! − 10 = −16 − 10  

    −16 − 10 = −26  

    so  the  result  for  the  top  is: − 26  

    5 + 3 5 − 4 = 5+ 3 1   5 + 3 1 = 5+ 3   5 + 3 = 8  

    so  the  result  for  the  bottom  is:  8  

    • !!!! !!!∙! !!! !!!

    = !!" ! = − !∙!"

    !∙! = − !"

    !

     

  • Lycée Jean-Piaget - Neuchâtel 2015-2016

    Mathematics 1MPES2 Chapter 1

    • !!! !!! !!!! !!!!

    =

    Top   Bottom  

    4 + 5 2 − 9 = 9 2 − 9  

    9 2 − 9 = 9 −7  

    9 −7 = −63  

    so  the  result  for  the  top  is: − 63  

    2! − 2 2! + 3 = 2! − 2 4 + 3  

    2! − 2 4 + 3 = 2! − 2 7  

    2! − 2 7 = 8 − 2 7  

    8 − 2 7 = 8 − 14  

    8 − 14 = −6  

     so  the  result  for  the  bottom  is:   − 6  

    • !!!! !!!∙! !!! !!!

    = !!" !!

    = !∙!" !∙!

    = !" !

    9.  Practical  exercises:  

    • !!!!!! !! !!!!!!

    =

    Top   Bottom  

    −2 + 5! − −1 = −2 + 25 − −1  

    −2 + 25 − −1 = −2 + 25 + +1  

    −2 + 25 + +1 = 24  

    so  the  result  for  the  top  is:  24  

    −2 + 1 − 5 = −1 − 5  

    −1 − 5 = −6  

    so  the  result  for  the  bottom  is:   − 6  

    • !!!!!! !! !!!!!!

    = !" !! = −4

     

    • !!! !"!! !!!!"

    = Top   Bottom  

    6 + 6 27 − 9 = 12 18  

    12 18 = 216  

    so  the  result  for  the  top  is:  216  

    6! − 12 = 36 − 12  

    36 − 12 = 24  

    so  the  result  for  the  bottom  is:  24  

    • !!! !"!! !!!!"

    = !"# !"

    = !∙!" !"

    = 9