This is Dr. Heinrich Zyphenblaza, infamous surgeon and renowned mathematician from the Googol Numerical Institute in Deusseldorf, Germany.

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This is the order of operations! Don’t go in a differ order or your pat will reall ! Don’t

important rule or you will be in trouble!

12

3

6

9

One day, long ago, Heinrich made a fateful mistake that would change the course of his life forever. Z z z z z …

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1. Put patient to sleep.

2. Make incision.

3. Fix problem.

4. Stitch up patient.

A few years ago, Dr. Zyphenblaza made a horrible and costly mistake. One morning, he forgot about the order in which an operation is done, and accidentally began operating on a poor patient before the anesthesiologist administered the anesthesia. Not only did he cause the patient excruciating pain, but he lost his license, too.

scalpelsponge

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Devastated and full of shame, Dr. Zyphenblaza retreated to his villa in the Alps. There, he regrouped and concentrated his mind and his efforts on making sure no one ever operated out of order again. He also studied mathematics extensively and discovered an interesting similarity.

Brrrr….

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I discovered that when presented with a mathematical

expression, I could get different results, depending on the order in which I performed

my calculations.

Let’s go to the whiteboard.

3+6x5

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3+6x5

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3+6x5=

9x5=

=45

3+6x5=

3+30=

=33

When I do the addition first, I get the answer

45.

When I do the multiplication first, I get the answer 33.

Do you see how the order in

which you work out the problem

is important?

Operations – The four mathematical operations are multiplication, division, addition and subtraction.

Order of Operations – The order of operations are a set of rules to follow for calculations involving more than one mathematical operation.

More

But, first, let’s make sure we know what

a mathematical operation is.

Therefore, the order of operations is

defined this way.

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So, just like in my medical training, the order of

operations for mathematics is important.

Parenthesis

Exponents

Multiplication and Division

Addition and SubtractionWhen performing the multiplication, division, addition, and subtraction, calculate from left to right, in the order that they appear.

First, calculate anything in

parenthesis. Then calculate the

expressions with exponents.

After taking care of those

calculations, perform the

multiplication and division, from left

to right, in the order that they

appear. Finally, execute the addition and

subtraction, from left to right, in the

order that they appear. Go On

3+6x5

3+6x5=

9x5=

=45

3+6x5=

3+30=

=33

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Let’s look at the problem and the

two solutions again.

Since there are no parenthesis or exponents in this problem, the first

step would be to perform the multiplication.

With that in mind, the second solution is the correct one because the multiplication was

done first and then the addition.

Let’s go back to the

operating room again.

(4+3)x2

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Of course! We do the arithmetic that is

within the parenthesis first. Then we multiply.

Here is another problem. Again, you will get different answers if you do not follow

the rules for the order of operations. So, where do we

start?

Observe.

Calculate (4+3) first Calculate 3x2 first

Nope. Remember to calculate what

is inside the parenthesis first.

Try again.

(4+3)

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x2( 7 )14

(4+3)x2=

(7)x2=

=14

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12-(5-3)2

Wow! This problem has parenthesis and

exponents! Remember, do the arithmetic within

the parenthesis first.

(5-3)2

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12-( 2 )28

12-(5-3)2 =

12-4 =

=8

12-(2)2 =

4

Then perform the operation

with the exponent.

Then, subtract.

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We have an emergency here! The parenthesis

contains more than one operation!

OH! Thank goodness we were able to revive him!

(6x2-3)

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-7( 12-3)2

(6x2-3)-7 =

9-7 =

=2

(12-3)-7 =

9

After you multiply, do the

subtraction within the parenthesis.

Then subtract.

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Today, I’ve demonstrated

various operations on different kinds of

expressions.

Now it’s your turn to put into practice what you have just

learned.

Let’s go to the whiteboard

again.

(8+3x5)+6/3

(8+15)+2=

23+2=

=25

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25 57 20 58

All right!

Try again.

Remember, do the arithmetic in the parenthesis first – the

multiplication must be performed before the addition. Then do the division and the addition located

outside of the parenthesis.

Click on the correct answer.

(6x9)/2-10

(54)/2-10=

27-10=

=17

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1746 3222

All right!

Try again.

Do the arithmetic within the parenthesis first and then

the division. Then subtract 10 from the result.

Here’s another problem.

3+(3x2)2-6/23+(6)2-6/2=

3+36-6/2=

3+36-3=

=36

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36

9

18

78

All right!

Try again.

Remember, do the arithmetic in the parenthesis first – the

multiplication must be performed before the addition. Then do the division and the addition located

outside of the parenthesis.

Let’s see what you can do with

this one.

9-3+4x2+1

9-3+8+1=

6+8+1=

=15

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15

30

13

21

All right!

Try again.

Since there are no parenthesis or exponents, the first thing you would calculate would be the

multiplication. Then, you would do the subtraction and addition

from left to right in the order that they appear.

And, one more.

(3x5)+(4-2)2-5x215+(2)2-

5x2=

15+4-10=

19-10=

=9

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9

28

13

7

All right!

Try again.

Calculate the expressions within the parenthesis first. Calculate

the expression with the exponent, next. Then perform the multiplication. Finally, do the addition and subtraction.

Last one!

Super job! Always remember the order of operations when

calculating mathematical expressions (or when operating on someone…). Good luck in

your numerical pursuits, and may all your operations be orderly!