What are the four tiers of BODMAS in order? �465 Brackets → Orders → ×÷ (l→r) → +− (l→r).
Which do you do first: the M or the D in BODMAS? ↔ Neither "first" — same tier, left to right.
Why do exponents beat multiplication? ↔ Exponent = repeated multiplication, a higher shorthand.
What does a fraction bar secretly do? ↔ Brackets the whole numerator and whole denominator.
−22=? ↔ −4, because the power binds before the minus.
In BODMAS, do division or multiplication come first?
Neither is inherently first — they share one tier and are done left to right.
Why must multiplication be done before addition?
Multiplication is repeated addition, so it must be fully computed (unpacked) before it can be added to anything.
Evaluate 2+3×4.
14 (do 3×4=12 first, then add 2).
Evaluate 20÷5×2.
8 (same tier, left to right: 20÷5=4, then ×2).
What is −32?
−9, because the exponent binds tighter than the unary minus.
What is (−3)2?
9, because the bracket forces the sign into the base first.
In nested brackets, which do you evaluate first?
The innermost bracket, because outer expressions depend on its value.
What grouping does a fraction bar impose?
It brackets the entire numerator and the entire denominator separately.
Evaluate 6+2[3+(4−1)2].
30.
Recall Feynman: explain to a 12-year-old
Imagine a recipe: "stir the sauce, THEN pour it on the pasta." If you pour first, you get a mess. Maths has a fixed recipe order too. Brackets are the chef shouting "do THIS bit first!" Powers are secret multiplications, and multiply/divide are done before add/subtract because they're bigger, packed-up jobs. When two jobs are equal size, you just read left to right, like reading a sentence. Follow the recipe and everyone in the world gets the same number.
Dekho, order of operations ek simple sa niyam hai jo batata hai ki expression ko kaunse order mein solve karna hai, taaki poori duniya ka jawab same aaye. BODMAS aur PEMDAS bas do naam hain ek hi rule ke. Sabse pehle Brackets, phir Orders (powers/roots), phir Multiply aur Divide, aur last mein Add aur Subtract.
Sabse important baat jo log galat samajhte hain: Multiply aur Divide ek hi level par hote hain — inme koi ek pehle nahi hota, jo pehle aaye (left to right) usse karo. Same cheez Add aur Subtract ke saath. Jaise 8−3+2 ka answer 7 hai, 3 nahi, kyunki left se right chalte hain. Aur "M pehle ya D pehle" wala confusion bilkul chhod do.
Powers, multiply se pehle kyun? Kyunki a3 ka matlab hai a×a×a — yaani power to multiply ka packed version hai, isliye pehle usse kholna padta hai. Isi tarah multiply, add ka packed version hai. Isliye ladder banti hai: pehle sabse bada packed operation kholo.
Nested brackets mein hamesha andar wale bracket se shuru karo, kyunki bahar wala uska answer use karta hai. Aur ek trap yaad rakho: −32=−9, lekin (−3)2=9 — bracket sign ko base ke andar force kar deta hai. Confusion ho to khud extra brackets laga do — safe rehta hai!
