Whilst doing my daily Facebook scrolls, I came across this post and when I went through the comments, I started to wonder why some people were getting the wrong solution.
I'm probably not ready for Harvard but I got a lil book sense. How about you?
Posted by ThisisLADY on Tuesday, July 15, 2014
Could it perhaps be due to cognitive biases or the mnemonic they were taught to remember what arithmetic operations have precedence over the others? Let me investigate...
The equation is 40 + 40 * 0 + 1
Solving this equation sequentially would give the wrong solution below.
40 + 40 = 80
80 * 0 = 0
0 + 1 = 1
Solving it using PEMDAS
P -- stands for parenthesis ( brackets)
E -- stands for exponents
M -- stands for multiplication (times)
D -- stands for division (divide)
A -- stands for addition (plus)
S -- stands for subtraction (minus)
The equation is 40 + 40 * 0 + 1
Solving this equation sequentially would give the wrong solution below.
40 + 40 = 80
80 * 0 = 0
0 + 1 = 1
If you have done any maths in school, you would have remembered that arithmetic operations are not solved sequentially but rather based on order of operations as identified by BODMAS and PEMDAS.
Solving it using PEMDAS
P -- stands for parenthesis ( brackets)
E -- stands for exponents
M -- stands for multiplication (times)
D -- stands for division (divide)
A -- stands for addition (plus)
S -- stands for subtraction (minus)
One popular mnemonic used to remember the order of operations is "Please Excuse My Dear Aunt Sally". Other great mnemonics are "Picking Eminem Made Dre A Star", "People Eat More Donuts After School", "Please Excuse My Dope Ass Swag".
There are no parenthesis in the equation, so we ignore the P
There are no exponents in the equation, so we ignore the E
There are no division in the equation, so we ignore the D
There are no subtraction, so we ignore the S
There is multiplication and addition. PEMDAS tells us we always multiply before adding.
40 + 40 * 0 + 1 = 40 + (40 * 0) + 1 = 40 + 0 + 1
The next thing to do is to do the A which is for addition
40 + 0 + 1 = 40 + 1 = 41
PEDMAS gives the solution of 41
Solving it using BODMAS
 |
| Arithmetic Order of Operation (BODMAS) |
B -- stands for brackets ()
O -- stands for others or order (exponents, square roots, factorial, etc)
D -- stands for division (divide)
M -- stands for multiplication (times)
A -- stands for addition (plus)
S -- stands for subtraction (minus)
The equation to solve is 40 + 40 * 0 + 1
Take note that there are no brackets, others (exponents), division and subtraction. All we have to do is multiply and add the numbers. BODMAS tells us that multiplication is done first before addition.
Therefore, 40 + 40 * 0 + 1 becomes 40 + 0 + 1. Now all we have to do is add the remaining numbers and get the answer of 41 which is the exact answer obtained using PEMDAS.
The two methods gives exactly the same answer. One thing to take note of is that PEMDAS gives precedence to multiplication over division whilst BODMAS gives precedence to division over multiplication.
Another example: 9 - 6 * 3^2 + 2 * (3 * 1/2)
Using PEMDAS
Start with parenthesis
9 - 6 * 3^2 + 2 * (3 * 1/2) = 9 - 6 * 3^2 + 2 * 3/2
Follow with exponents
9 - 6 * 3^2 + 2 * 3/2 = 9 - 6 * 9 + 2 * 3/2
Next is multiplication
9 - 6 * 9 + 2 * 3/2 = 9 - (6 * 9) + (2 * 3)/2 = 9 - 54 + 6/2
Next is division
9 - 54 + 6/2 = 9 - 54 + 3
Addition follows
9 - 54 + 3 = 9 + (-54 + 3) = 9 - 51
Finally subtraction
9 - 51 = -42
Using BODMAS should also use give the exact same solution.
Another example: 9 - 6 * 3^2 + 2 * (3 * 1/2)
Using PEMDAS
Start with parenthesis
9 - 6 * 3^2 + 2 * (3 * 1/2) = 9 - 6 * 3^2 + 2 * 3/2
Follow with exponents
9 - 6 * 3^2 + 2 * 3/2 = 9 - 6 * 9 + 2 * 3/2
Next is multiplication
9 - 6 * 9 + 2 * 3/2 = 9 - (6 * 9) + (2 * 3)/2 = 9 - 54 + 6/2
Next is division
9 - 54 + 6/2 = 9 - 54 + 3
Addition follows
9 - 54 + 3 = 9 + (-54 + 3) = 9 - 51
Finally subtraction
9 - 51 = -42
Using BODMAS should also use give the exact same solution.
