Ch 1: Number System & Simplification (BODMAS)

01 — NOTES

Poore notes, ek-ek karke

5 chhote lessons aur labs — padho, phir khud khel ke pakka karo.

00

Introduction — Maths ki neev

Maths ka safar yahin se shuru hota hai. Ye chapter numbers ke types (natural, whole, prime…), place value, divisibility rules, BODMAS, sum formulas aur unit digit cover karta hai. CET mein simplification/number system ke sawal lagbhag pakke hote hain — aur ye sabse aasan marks hain, bas rules yaad hone chahiye.

Upar Formula Lab mein slider khiskao — answer turant badalta hai. Pehle BODMAS ka poora khel step-by-step dekho:

Lab 1

BODMAS stepper — ek sawal, har step

8 steps

01

Numbers ke types 🔢

Type	Kya hota hai	Examples
Natural	Ginti ke numbers — 1 se shuru	1, 2, 3, …
Whole	Natural + 0	0, 1, 2, …
Integers	Whole + negative	…, −2, −1, 0, 1, 2, …
Even / Odd	2 se divide / nahi	2, 4, 6 · 1, 3, 5
Prime	Sirf 2 factors — 1 aur khud	2, 3, 5, 7, 11, 13
Composite	2 se zyada factors	4, 6, 8, 9, 10
Co-prime	Do numbers jinka HCF = 1	(4, 9), (8, 15)

1 na prime hai na composite · 2 aklauta even prime · 0 whole hai, natural nahi · sabse chhota composite = 4.
1 se 100 tak 25 primes (1 se 50 tak 15): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 · 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Face value = digit khud · Place value = digit × jagah. 25,634 mein 5: face value 5, place value 5000.

Lab 2

Prime ya Composite?

12 numbers

Prime sirf 1 aur khud

Composite aur bhi factors

Upar se koi number chuno, phir sahi dabbe par tap karo.

02

Divisibility rules ⚠️ exam favourite

Number	Rule	Example
2	Last digit even	128 ✓
3	Digits ka sum 3 se divide	456 → 15 ✓
4	Last 2 digits 4 se divide	716 → 16 ✓
5	Last digit 0 ya 5	435 ✓
6	2 aur 3 dono se	132 ✓
8	Last 3 digits 8 se divide	5104 → 104 ✓
9	Digits ka sum 9 se divide	45783 → 27 ✓
11	(Odd places ka sum) − (Even places ka sum) = 0 ya 11 ka multiple	245157 → 12 − 12 = 0 ✓

✏️ Solved — 11 ka rule245157: odd places (right se 1st, 3rd, 5th) = 7 + 1 + 4 = 12 · even places = 5 + 5 + 2 = 12 · difference 0 → divisible ✓

03

BODMAS — simplification ka master rule

Order	Letter	Matlab
1	B — Bracket	( ) → { } → [ ] · bar (line) sabse pehle
2	O — Of	"of" = multiply, lekin ÷ se bhi pehle
3–4	D, M	÷ aur × barabar — left se right jo pehle aaye
5–6	A, S	+ aur − barabar — left se right

12 + 8 ÷ 4 × 3 − 5 → 8 ÷ 4 = 2 → 2 × 3 = 6 → 12 + 6 − 5 = 13.
"Of" ka trap: 18 ÷ 3 of 2 = 18 ÷ 6 = 3 · lekin 18 ÷ 3 × 2 = 6 × 2 = 12.
Minus ke baad bracket khule to andar ke saare sign ulte: 10 − (4 − 6) = 10 + 2 = 12.

04

Sum formulas aur unit digit 🔁

Series	Formula	Example
1 + 2 + … + n	n(n+1)/2	1–50 = 1275
1² + 2² + … + n²	n(n+1)(2n+1)/6	1–10 = 385
1³ + 2³ + … + n³	[n(n+1)/2]²	1–5 = 225
Pehle n odd	n²	pehle 20 = 400
Pehle n even	n(n+1)	pehle 15 = 240

Digit	Unit digit cycle	Length
0, 1, 5, 6	Hamesha wahi digit	1
4 · 9	4, 6 · 9, 1	2
2 · 3	2, 4, 8, 6 · 3, 9, 7, 1	4
7 · 8	7, 9, 3, 1 · 8, 4, 2, 6	4

✏️ Solved — 7⁴⁵ ka unit digit7 ka cycle 7, 9, 3, 1 · 45 ÷ 4 → remainder 1 → cycle ka 1st digit = 7. (Remainder 0 ho to cycle ka last digit.)

Lab 3

Sawal → answer

10 rounds

02 — EXAM

Exam mein kya poochha jata hai

CET mein isi chapter se yahi patterns aate hain.

TYPE 1

"Simplify karo"

BODMAS — bracket, of, phir ÷/× left se right, phir +/−.

TYPE 2

"Divisible kaunsa?"

3/9 = digit sum · 4 = last 2 · 8 = last 3 · 11 = odd − even places.

TYPE 3

"Unit digit of aⁿ"

Cycle (length 4) · power ÷ 4 ka remainder · 0 → last digit.

TYPE 4

"Sum of first n…"

n(n+1)/2 · odd = n² · even = n(n+1).

TYPE 5

"Prime / face value ka fact"

1 neither · 2 only even prime · 1–100 mein 25 primes · place value = digit × jagah.

03 — TRICKS

Yaad rakhne ki desi tricks

Ratta nahi — connect karke yaad karo.

TRICK 1 · n5²

n × (n+1) | 25

35² → 3 × 4 = 12 → 1225 · 75² → 7 × 8 = 56 → 5625. 2 second ka kaam!

TRICK 2 · ×999

×1000 − ×1

47 × 999 = 47000 − 47 = 46953 · 47 × 99 = 4700 − 47 = 4653.

TRICK 3 · ×5, ×25

×5 = ×10 ÷ 2

84 × 5 = 840 ÷ 2 = 420 · 36 × 25 = 3600 ÷ 4 = 900.

TRICK 4 · PRIME CHECK

2, 3, 5, 7 se test

100 tak ke number ko sirf in chaar se divide karke dekho. 91 = 7 × 13 — prime nahi!

TRICK 5 · BRACKET ORDER

"Chhota bracket, pehla number"

( ) → { } → [ ] — andar se bahar. Bar/line wala bracket sabse pehle.

04 — COMMON MISTAKES

Yahan marks katte hain

Har card par galat baat likhi hai. Tap karke sach dekho.

✗ GALAT

"BODMAS mein hamesha pehle ÷ hota hai."

tap karo →

✓ SAHI

÷ aur × barabar — jo left mein pehle. 12 × 8 ÷ 4 × 2 = 48, 12 nahi.

✗ GALAT

"1 sabse chhota prime hai."

tap karo →

✓ SAHI

1 na prime na composite. Sabse chhota prime = 2.

✗ GALAT

"18 ÷ 3 of 2 = 12."

tap karo →

✓ SAHI

"Of" pehle: 3 of 2 = 6 → 18 ÷ 6 = 3.

✗ GALAT

"10 − (4 − 6) = 10 − 4 − 6 = 0."

tap karo →

✓ SAHI

Minus ke baad bracket → sign ulte: 10 − 4 + 6 = 12.

✗ GALAT

"25,634 mein 5 ki place value 5 hai."

tap karo →

✓ SAHI

5 = face value. Place value = 5 × 1000 = 5000.

05 — FLASHCARDS

20 cards, 3D deck

Card par tap karke palto. Next → se agla card, ← Previous se pichhla. Yaad ho gaya to "Yaad hai" dabao — wo card deck se hat jayega. Keyboard: ← → , space (palto), Enter (yaad hai).

06 — REVISION

2-minute revision

Exam se pehle bas ye list. Kuch bhi search karo — "prime", "BODMAS", "cycle"…

Sabse chhota prime2 (aklauta even prime)

Sabse chhota odd prime3

Sabse chhota composite4

1 kya hai?Na prime, na composite

0 natural hai?Nahi — whole hai

Primes 1–50 / 1–10015 / 25

1 se 100 tak sum5050

1 + … + nn(n+1)/2

1² + … + n²n(n+1)(2n+1)/6

Pehle n odd / evenn² / n(n+1)

BODMAS mein "of"÷ se pehle

÷ aur × mein pehleJo left mein pehle aaye

3 aur 9 ka ruleDigits ka sum

11 ka ruleOdd − even places = 0 ya 11k

0, 1, 5, 6 ka unit digitKisi bhi power par wahi

7 ka cycle7, 9, 3, 1

07 — QUIZ

Practice MCQs — game mode

14 exam-style questions (PYQ wale tagged hain), ek-ek karke — koi question nahi aata to Skip karke aage badho. Har sahi answer +5 XP, lagatar sahi par combo. 10+ laao aur quiz mission complete karo.

08 — SUMMARY

Poora chapter, ek paragraph mein

Numbers: 1 na prime na composite, 2 aklauta even prime, 0 natural nahi; 1–100 mein 25 primes. Divisibility: 3/9 = digit sum, 4 = last 2, 8 = last 3, 11 = odd − even places. Simplification ka boss BODMAS — bracket pehle, "of" ÷ se pehle, ÷/× mein jo left mein pehle. Sum: 1 se n = n(n+1)/2, pehle n odd = n². Unit digit: cycle of 4, remainder 0 → last digit. Tricks (n5², ×999, ×25) roz 5 sawalon par practice karo — speed apne aap banegi! 🚀

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Next: HCF & LCM →

Bade numbers ka HCF-LCM, bells aur tiles wale sawal — Chapter 2.

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Number System & BODMAS

Notes padho

3 labs chalao

Flashcards

Quiz 10+/14

Chapter complete

Poore notes, ek-ek karke

Introduction — Maths ki neev

BODMAS stepper — ek sawal, har step

Numbers ke types 🔢

Prime ya Composite?

Prime sirf 1 aur khud

Composite aur bhi factors

Divisibility rules ⚠️ exam favourite

BODMAS — simplification ka master rule

Sum formulas aur unit digit 🔁

Sawal → answer

Exam mein kya poochha jata hai

Yaad rakhne ki desi tricks

Yahan marks katte hain

20 cards, 3D deck

2-minute revision

Practice MCQs — game mode

Poora chapter, ek paragraph mein

Chapter khatam?

Next: HCF & LCM →

Aage ke chapters kholo