# 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

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