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