PYTHON BODMAS

Week A16: 17th-23rd Feb2025

• B — Bracket (parenthesis)
• O — Order ( exponent)
• D — Division
• M — Multiplication
• A — Addition
• S — Subtraction

BODMAS is just a trick or concept to remember the precedence order in mathematics.

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This is precedence order and the operations associvity

• parenthesis `()` has highest precedence (level 1) and works from inwards to outwards parenthesis in nested parenthesis, and has left to write association
• exponent `**` has second highest precedence (level 2) and right to left association
• unary operations like `+x, -x, ~x` has next level precedence (level 3) and right to left association
• division `\`, multiplication `*`, floor division `\\`, modulus `%` has same precedence (4) and left to right association.
• addition `+` and subtraction `-` has level 5 precedence and left to right association.

Some notes

• Python follows left to right order in most cases.
• unary operations means it only affects one operand unlike other operations which operates between two operands
• unary operations `x = 5 then -x ==> -5 `
• subtraction operation `x = 5 , y = 3 then x-y ==>2`

# SIMPLE ADDITION
1+2+3+4+5
output
>>> 15 

* It has left to right association so,
* It goes 1+2 →3 +3 →6 +4 →10 +5 →15

# SIMPLE SUBRACTION
10-2-3-4-5
output>>> -4

* It also has left to right association
* It goes 10-2-->8 -3 -->5 -4 -->-1 -5-->-4

# SIMPLE MULTIPLICATION
1*2*3*4*5
output>>> 120

* It goes 1*2-->2 *3-->6 *4 -->24 *5 -->120
* It also has left to right association

# SIMPLE DIVISION
24/4/3/2
output>>> 120

* It goes 24/4 -->6 /3 -->2 /2-->1
* It also has left to right association

# SIMPLE EXPONENTIAL
2**3**2
output>>> 512

* It goes 2**(3**2)--> 2**9 -->512
* It has right to left association

# SOLVING COMPLEX EXPRESSIONS utilising above simple calculation
2 + 3**2**2 /3 -(5 *3)  - 6 / 10 * 4/30 *25 + 5 - 10 
output>>> 7 

series of conversions
step1: evaluates paranthesis `5*3 = 15` then the above expression becomes

    2 + 3**2**2/3 -15 -6 / 10 * 4 / 30 * 25 + 5 - 10

step2: evaluates exponential from right to left `==> 3**2**2 ==>3**4==>81`
    
    2 + 81/3 -15 -6 /10 * 4 / 30 * 25 + 5 - 10

step3: evaluates multiplication and division from left to right as 
       they have same precedence and
`81/3 ==>27`, `6/10 = 0.6`, `0.6*4 = 2.4`, `2.4/30 = 0.08`,`0.08*25 = 2`
the eqn becomes 

    2 + 27 -15 - 2 + 5 -10 

step4: evaluates addition and subraction from left to right 

`2 + 27 = 29`, `29-15 = 14`,`14-2 = 12`, ` 12+5 = 17` , `17-10 = 7`

therefore the final result is  7