This is Dr. Heinrich Zyphenblaza, infamous surgeon and renowned mathematician from the Googol Numerical Institute in Deusseldorf, Germany. Go On
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 … Go On 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. scalpel sponge Go On
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…. Go On
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 Go On
3+6x5 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. Go On So, just like in my medical training, the order of operations for mathematics is important.
Parenthesis Exponents Multiplication and Division Addition and Subtraction When 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 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 Go On 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) firstCalculate 3x2 first Nope. Remember to calculate what is inside the parenthesis first. Try again.
Go On 12-(5-3) 2 Wow! This problem has parenthesis and exponents! Remember, do the arithmetic within the parenthesis first.
(5-3) 2 Go On 12-( 2 ) 2 8 12-(5-3) 2 = 12-4 = =8 12-(2) 2 = 4 Then perform the operation with the exponent. Then, subtract.
Go On We have an emergency here! The parenthesis contains more than one operation! OH! Thank goodness we were able to revive him!
(6x2-3) Go On -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.
Go On 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 Go On 25572058 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 Go On 17463222 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 -6/2 3+(6) 2 -6/2= 3+36-6/2= 3+36-3= =36 Go On 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 Go On 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 -5x2 15+(2) 2 -5x2= 15+4-10= 19-10= =9 Go On 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!