order of operations

Order of Operations

aka: PEMDAS

Beth Rickerts 6th Grade NW Guilford Middle School 2011

Students come to sixth grade thinking they know PEMDAS.

But do they know WHY they excuse Aunt Sally?

Of course! For looking too rough! Poor Aunt Sally.

From Left To Right

FOR LOOKING TOO ROUGH?

But what does PEMDAS FLTR really mean?

It means that mathematicians have all agreed that to solve for a non-algebraic equation or expression, we ALL follow the same steps.

We follow an order and we then we work from left to right, just as when we are reading.

Penguins???Penguins Eat Delicious Minnows Swimming Around

BUT WHY AUNT SALLY?Why not ….

Parenthesis Exponents Division and Multiplication From Left to

Right Subtraction and Addition From Left to Right

Would this work????

PEDMSA???

I mean who decided it was Aunt Sally and not PENGUINS????

Regardless of your preference, all mathematicians follow the same rule and

that is Parenthesis FIRST. Exponents SECOND.

And then…it’s up to you to pick out the operators.

Just like in hopscotch, the first two squares must stand alone.

Parenthesis Exponents

Then you get to pick which square to hop in…multiplication or division….addition or subtraction..

One at a time, from left to right, Multiplication or Division

One at a time, from left to right, Addition or Subtraction

Order of Op Hop…..

( )

NE

X ÷

+ -

Order of Op Hop-Scotch

( )

NE

÷ X

- +

32(12 – 4)- 8 ÷ ½ + 6

Besides the order, it is important to remember these two mantras:

◈Work it out ONE STEP AT A TIMEand

◈ Focus on the operators

Order of Operations

32(12 – 4)- 8 ÷ ½ + 632(8) - 8 ÷ ½ + 6

9(8)- 8 ÷ ½ + 672 – 8 x ½ + 6

72 – 4 + 668 + 6

74

It should look like a slice of pizza when you are finished!

ONE STEP AT A TIME

Step Parenthesis (12-4)Step Exponent 32

Step Multiplication and/or Division from left to right

9 x 8 and 8 x ½ Step Addition and/or

Subtraction from left to right

72 – 4 and finally add 68 + 6 for 74.

Did you follow the correct steps?

81 ÷ 9(2) – 24 + (5-3)

ONE OPERATION AT A

TIME

Focus on the operators.

81 ÷ 9(2) – 24 + (5-3)81 ÷ 9(2) – 24 + 281 ÷ 9(2) – 16 + 2

9 (2) – 16 + 218 -16 + 2

2 + 24

One Step at a Time

12 (5) – (6 ∙ 22 ÷ 3) +50

2

Do NOT be tempted to work more than ONE

operator at a time. You are going for a nice

triangular shape and if you do two operators at

a time you could be setting yourself up for a

careless error!

Did you get 23?

12 (5) – (6 ∙ 22 ÷ 3) +50

212 (5) – (6 ∙ 4 ÷ 3) +50

212 (5) – (24÷ 3) +50

212 (5) – (8) +50

212 (5) – 8 + 1

26(5) – 8 + 130 – 8 + 1

22 + 123

Your Turn

Sometimes you might come across 2 parenthesis or brackets. Work from inside

out…

7 +[7 x ( 4 + 6 ) 2 ] + 77 + [7 x (10) 2 ] + 77 + [ 7 x 100] + 7

7 + 700 + 7707 + 7

714

Double Parenthesis and Brackets

If you see a problem that is over a whole number then you will need to solve for all of

the numerator first before dividing by the denominator.

4 (2+3)( 1 + 2 x 3)+ 120 – 32

6

Or it could be just a fraction in your problem which would simply be a division problem.

Pay attention!

Fractional Parts

1. ( 8 ÷ 4 ) 2 + ((10 + 5 ) + 32 )

2. (16 - 5 ) +(12 ÷ 2 ) 2 + 70

3. 14 +( ( 1+ 2 ) 3 ÷ 9 ) - 44. (16/4) - (24 ÷ 8 ) x 52

5. ( 5 +4 ) 2 + 7 – 13 5

Practice PEMDAS