Ungliyan, Tally Aur 2 Se Ginti | Class 8 Maths Book 1 Ch 3

📘 Class 8 · Ganita Prakash Book 1Ch 3 · A Story of NumbersPost 2 / 8⏱ 25–30 min

Ungliyan, Tally Aur 2 Se Ginti 🦴

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

One-to-one mapping kya hai?
Tally mein 5 kaise banate ho?
2 + 2 + 2 + 1 = ?

Answers dekho

Har cheez ki ek alag jodi
Chaar khadi lakeer + ek tirchhi (||||/)
7

Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 1 — Ginti Ki Shuruaat Kaise Hui? dobara padh lijiye.

— 📌 charumam.com

🎬 Kahani: Cricket Ka Scorer Aur Ek Nazar Ka Khel

Gali cricket mein Ishaan scorer bana. Har run pe chalk se ek lakeer: | | | | | | | | | | | | | | | | | … Over khatam hone tak deewar pe 37 lakeerein! Ab gino. 😵

Uski didi aayi aur boli: “Har paanchvi lakeer tirchhi kaato, gate bana do: ||||/.” Ab sirf gate gino aur bachi lakeerein.

Yeh chhoti si trick 20,000 saal purani hai! Aur iske peeche ek dimaag ki seema chhupi hai. Chaliye dekhte hain kya. 🧠

— 📌 charumam.com

📖 Concept: Nishaan Se Group Tak

💡 Is post ki ek badi baat: Har cheez ka ek nishaan (tally) ginti hai, par group banaana use tez aur saaf karta hai. Ek group ko ek naya naam ya chinh do: yahi aage chalkar “base” ka beej hai.

Step 1: Shareer se ginti

Papua New Guinea ke kuch samudaay aaj bhi ungliyon se shuru karke kalaai, kohni, kandha, kaan, aankh… tak shareer ke hisse ek fixed kram mein ginte hain. Shareer = unka standard sequence.

WHY kaam karta hai? Har hissa hamesha same jagah, same kram mein: one-to-one milaan (Post 1 — Ginti Ki Shuruaat Kaise Hui?) ke liye perfect, aur kuch le jaana nahi padta!

Step 2: Haddi pe nishaan (tally marks)

Har cheez ke liye ek kaat. Kaaton ka dher = ginti. Yeh lakdi wale method jaisa hi, bas kaat pakki hai, gire nahi.

Lebombo haddi (dakshin Africa): 29 kaat, lagbhag 44,000 saal purani. Shayad chaand ka calendar!
Ishango haddi (Congo): 20,000–35,000 saal purani, kaat column mein.

WHY 29? Chaand ka ek chakra (amaavasya se amaavasya) ≈ 29.5 din. Isliye log ise calendar maante hain.

Step 3: Ek nazar ki seema

Bina gine kitne bindu dikhte hain? ● ● ● → turant 3. ● ● ● ● ● ● ● → ruk ke ginna padta hai.

Zyaadatar log 4 tak ek nazar mein pehchaan lete hain; 5 ya zyada pe ginna padta hai.

WHY yeh important? 37 lakeerein ek nazar mein nahi dikhti. Isliye log har 5 pe nishaan badal dete hain (||||/): ab har gate ek nazar mein “5” hai.

Step 4: 2-2 mein naam: Gumulgal

Australia ke Gumulgal log: urapon = 1, ukasar = 2. Phir 3 = ukasar-urapon, 4 = ukasar-ukasar, 5 = ukasar-ukasar-urapon, 6 = ukasar-ukasar-ukasar. 6 se zyada = “ras” (bahut).

Hairaani: South America ke Bakairi aur Africa ke Bushmen ke paas bhi bilkul aisa 2-2 wala system tha, bina kabhi mile! Ek theory: inke poorvaj ek the.

WHY 2 se behtar? 6 ke liye 6 alag nishaan nahi, sirf 3 baar “ukasar”. Group size ka naam use karke bade number banaye.

Step 5: Group size: 2, 5, 10, 20

Alag-alag logon ne alag group size chune: 2 (Gumulgal), 5 (ek haath, Roman V), 10 (do haath), 20 (haath + pair). Kab kaunsa? Chhota group (2) = naam lambe; bada group (20) = zyada alag naam yaad karne padte. 5 aur 10 beech ka santulan.

🪜 Atak Gaye? Aise Socho

Lakeerein ginni hain? Pehle 5-5 ke gate banao.
Gate gino, × 5 karo, phir bachi lakeerein jodo.
Gumulgal naam banana hai? Pehle number ko 2 + 2 + … (+ 1) mein todo.
Har “2” ke liye ukasar, aakhri “1” ke liye urapon.
Ek nazar mein 4 se zyada nahi dikhta: isliye group banaana zaroori.

— 📌 charumam.com

🔐 Deep Concept: Hum 5 Pe Gate Kyun Banaate Hain? (Grouping Ka Beej)

Ek nazar mein ~4 cheezein pehchaanna dimaag ki seema hai. Agar group 10 ka banaate (|||||||||/) to woh gate bhi ek nazar mein nahi dikhta! 5 ka gate (4 khadi + 1 tirchhi) theek us seema ke andar hai: 4 lakeerein ek nazar mein, aur tirchhi batati hai “group poora”.

Grouping kya karti hai? Bade dher ko chhote, jaane-pehchaane tukdon mein todti hai. 37 = 7 gate + 2. Ab 37 cheezein nahi, 9 cheezein gin rahe ho!

Agla kadam socho: agar gate bhi bahut ho jaayein (100 gate)? To 5 gate ka ek “bada gate” bana do! Group ke group: 1, 5, 25, 125… Yahi “base” ka idea hai (Post 4 — Number System Mein Base Kya Hai?).

Unifying idea: ginti ka poora itihaas = “kitni baar group banaao, aur har group ko kya naam do”. 🎯

sirf charumam.com readers ke liye 🔐

✏️ Solved Examples

Example 1 (Easy): Ishaan ke 37 run tally mein kaise likhein? 5-gate se ginti check karo.

37 = 5 × 7 + 2 → 7 gate (||||/) + 2 lakeer (||).

Check: 7 × 5 = 35, + 2 = 37 ✅

📌 charumam.com

Example 2 (Medium): Gumulgal tareeke se 9 ka naam (agar woh 6 pe na rukte)?

9 = 2 + 2 + 2 + 2 + 1 → ukasar-ukasar-ukasar-ukasar-urapon.

Check: 4 ukasar = 8, + urapon 1 = 9 ✅

📌 charumam.com

Example 3 (NCERT style): Ek shepherd ne haddi pe 5-5 ke gate banaye: 12 gate aur 3 akeli kaat. Kitni bhedein?

12 × 5 + 3 = 63 bhedein.

Check: 63 ÷ 5 = 12 shesh 3: wahi gate aur akeli kaat ✅

📌 charumam.com

Ishaan ka scoreboard: didi ke gate ke baad 37 run = 7 gate + 2. Ab har baar total ek nazar mein! Ishaan ne kaha: “Yeh to 20,000 saal purani app hai!” 📱😄

— 📌 charumam.com

🏠 Aaj Bhi Tally Aur Grouping

🗳️ Vote ginti: chhote chunaav (school captain) mein aaj bhi 5-gate wale tally se ginte hain.
🏏 Scorebook: purane scorer har over ke 6 gend ke liye chhote nishaan lagaate the.
📦 Dukaan ka maal: kele “darjan” (12) mein, ande “tray” (30) mein: grouping se ginti tez.
🧘 Mala: 108 manke ki mala mein bade manke beech-beech mein: groups pehchaanne ke liye.
🎲 Paase: 1 se 6 ke bindu aise lagaaye jaate hain ki ek nazar mein dikh jaayein; 5 = 4 kone + 1 beech.

Jahan bhi “paanch-paanch” ya “darjan” mein ginte ho, wahan grouping ka jaadu hai.

— 📌 charumam.com

🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Chhoti ginti, record chahiye	✅ Tally (\|\|\|\|/)	Har 5 pe gate
Bahut badi ginti (10,000)	❌ Tally thaka dega	Group ke group chahiye
Bina kuch likhe ginti	✅ Ungli/shareer	Fixed kram
Chhote number ka naam	✅ 2-2 mein (Gumulgal)	Par 6 ke baad lamba
Ek nazar mein pehchaan	✅ 4 tak	Usse zyada pe group

— 📌 charumam.com

❌→✅ Worked Mistake

Sawaal: Tally ||||/ ||||/ ||||/ |||| — kitne?

❌ Galat: “4 gate = 20.” Aakhri group mein tirchhi lakeer nahi hai: woh gate poora nahi!

✅ Sahi: 3 poore gate (15) + 4 = 19. Check: kul lakeerein gino: 5 + 5 + 5 + 4 = 19 ✅

Doosri common galti: gate mein tirchhi ko alag gin dena (har gate = 6). Tirchhi khud 5vi cheez hai, extra nahi.

🧠 Rule of thumb: Gate = 4 khadi + 1 tirchhi = 5, tirchhi bhi ginti mein. Tirchhi nahi to gate nahi.

sirf charumam.com pe milenge!

📝 10 MCQs

Q1. Tally mein ||||/ ||||/ || = ?

(a) 10

(b) 12

(c) 14

(d) 7

Solution dekho

Sahi jawab: (b)

(a) galat: Aakhri do lakeerein bhi jodni thi.
(b) sahi: 2 gate (10) + 2 = 12 ✅
(c) galat: Har gate ko 6 maan liya: tirchhi extra nahi.
(d) galat: Gate aur lakeer ko barabar gin liya.

Q2. Lebombo haddi pe kitne kaat?

(a) 10

(b) 29

(c) 100

(d) 5

Solution dekho

Sahi jawab: (b)

(a) galat: 10 kaat wali haddi nahi hai yeh.
(b) sahi: 29 kaat: shayad chaand ka chakra ✅
(c) galat: 100 kaat itihaas mein nahi likhe.
(d) galat: 5 to sirf ek tally gate hai.

Q3. Gumulgal mein “ukasar” = ?

(a) 1

(b) 2

(c) 3

(d) 6

Solution dekho

Sahi jawab: (b)

(a) galat: 1 = urapon hai, ukasar nahi.
(b) sahi: Gumulgal mein ukasar = 2 ✅
(c) galat: 3 = ukasar-urapon (do shabd).
(d) galat: 6 = teen baar ukasar, ek shabd nahi.

Q4. Zyaadatar log ek nazar mein kitne tak pehchaante?

(a) 2

(b) 4

(c) 10

(d) 20

Solution dekho

Sahi jawab: (b)

(a) galat: 2 se zyada bhi ek nazar mein dikhte.
(b) sahi: Lagbhag 4 tak, phir ginna padta ✅
(c) galat: 10 ek nazar mein nahi dikhte.
(d) galat: 20 to bilkul ek nazar mein nahi.

Q5. Gumulgal mein 5 ka naam?

(a) ukasar-ukasar

(b) ukasar-ukasar-urapon

(c) urapon ×5

(d) ras

Solution dekho

Sahi jawab: (b)

(a) galat: Yeh 4 hai, ek urapon kam.
(b) sahi: 2 + 2 + 1 = 5, sahi naam ✅
(c) galat: Woh 2-2 mein ginte the, 1-1 mein nahi.
(d) galat: Ras 6 se zyada ke liye tha.

Q6. 5-gate wale tally se 43 ke kitne gate?

(a) 8 gate + 3

(b) 9 gate

(c) 4 gate + 3

(d) 43 gate

Solution dekho

Sahi jawab: (a)

(a) sahi: 8 × 5 = 40, + 3 = 43 ✅
(b) galat: 9 gate = 45, do zyada.
(c) galat: 4 gate = 20: 10 se bhaag kiya.
(d) galat: Har lakeer ko gate maan liya.

Q7. Grouping ka sabse bada fayda?

(a) Rang

(b) Kam cheezein ginni padti

(c) Number chhota hota

(d) Kuch nahi

Solution dekho

Sahi jawab: (b)

(a) galat: Rang ka ginti se lena-dena nahi.
(b) sahi: Bada dher chhote groups mein: tez ginti ✅
(c) galat: Number wahi rehta, likhne ka tareeka badla.
(d) galat: Ginti saaf aur tez hoti hai.

Q8. Teen door ke samudaay ke 2-2 wale systems same kyun? Ek theory?

(a) Copy kiya

(b) Common poorvaj

(c) Sanyog

(d) TV se

Solution dekho

Sahi jawab: (b)

(a) galat: Unka aapas mein koi sampark nahi tha.
(b) sahi: Ek theory: common poorvaj ✅
(c) galat: Sanyog ek sambhaavna, par theory poorvaj ki.
(d) galat: Us zamaane mein TV tha hi nahi.

Q9. Paase pe 5 ke bindu kaise hote?

(a) Line mein 5

(b) 4 kone + 1 beech

(c) Gol

(d) Random

Solution dekho

Sahi jawab: (b)

(a) galat: Line mein 5 ek nazar mein mushkil.
(b) sahi: 4 kone + beech: ek nazar mein ✅
(c) galat: Gol mein bhi ginna padta hai.
(d) galat: Random bindu pehchaanna mushkil.

Q10. ||||/ ka tirchhi wala nishaan kitna?

(a) 0

(b) 1

(c) 5

(d) 6

Solution dekho

Sahi jawab: (b)

(a) galat: Tirchhi bhi ek cheez ginti mein aati hai.
(b) sahi: Tirchhi = 5vi cheez, yaani 1 ✅
(c) galat: Poora gate 5, sirf tirchhi nahi.
(d) galat: Gate 6 nahi hota, 5 hota.

— 📌 charumam.com

❓ FAQs (Bachchon Ke Asli Sawaal)

1. Kya tally aaj bhi use hota hai?

Haan: chhote chunaav, kheliyon ka score, traffic survey mein gaadiyon ki ginti.

2. Kuch desh mein tally alag dikhta hai?

Haan! China-Japan mein 正 chinh 5 strokes ka: har stroke ek ginti. Idea same: 5 ka group.

3. “Ek nazar ki ginti” ka naam?

Ise subitizing kehte hain: bina gine turant pehchaanna.

4. Gumulgal 6 pe kyun ruke?

Shayad roz ki zindagi mein utna kaafi tha. Iske aage “ras” (bahut) se kaam chal jaata tha.

5. Haddi pe calendar kaise?

Har din ek kaat. 29–30 kaat pe chaand ka ek chakra poora: agla tyohaar ya mausam ka andaaza.

6. Ungliyon pe 10 se aage kaise ginein?

Har 10 pe ek pair ki ungli ya ek kankad alag rakh do: yahi “10 ka group” hai, base-10 ka beej.

— 📌 charumam.com

🏋️ Practice Zone (12 Sawaal)

Q1. Easy ||||/ ||||/ ||||/ | = ?

Solution dekho

15 + 1 = 16. Check: 3 × 5 + 1 ✅

Q2. Easy 28 ko 5-gate tally mein likho.

Solution dekho

5 gate + |||. Check: 25 + 3 = 28 ✅

Q3. Easy Gumulgal mein 4 ka naam?

Solution dekho

ukasar-ukasar. Check: 2 + 2 = 4 ✅

Q4. Easy ukasar-ukasar-urapon = ?

Solution dekho

5. Check: 2 + 2 + 1 ✅

Q5. Medium Gumulgal tareeke se 11 ka naam (6 pe na rukein to)?

Solution dekho

5 baar ukasar + urapon. Check: 10 + 1 = 11 ✅

Q6. Medium Ek haddi pe 9 gate aur 4 kaat. 2 aur din ke baad tally kaisa?

Solution dekho

9 × 5 + 4 = 49; 49 + 2 = 51 = 10 gate + 1. Check: 51 ÷ 5 = 10 shesh 1 ✅

Q7. Medium 5-gate tally mein 100 likhne ke liye kitni lakeerein (tirchhi bhi)?

Solution dekho

100 (har cheez ek lakeer). WHY: gate sirf dikhne ka tareeka, ginti nahi badalti. Check: 20 gate × 5 = 100 ✅

Q8. Medium Gumulgal mein (ukasar-ukasar-urapon) + (ukasar-urapon) = ? Bina 0–9 ke socho.

Solution dekho

Saare ukasar ek saath (3), saare urapon (2). 2 urapon = 1 ukasar → 4 ukasar = ukasar-ukasar-ukasar-ukasar (8). Check: 5 + 3 = 8 ✅

Q9. NCERT style Agar tally 5 ki jagah 3 ka gate (||/) ho, to 20 kaise likhoge? 5-gate se tulna karo.

Solution dekho

20 = 6 gate + 2 lakeer (9 cheezein gino); 5-gate mein 4 gate (4 cheezein). WHY: group bada = kam gate. Check: 6 × 3 + 2 = 20 ✅

Q10. NCERT style Gumulgal 2-2 mein ginte. Agar woh 4-4 mein bhi naam dete (“bada-ukasar” = 4), to 11 ka naam?

Solution dekho

11 = 4 + 4 + 2 + 1 → bada-ukasar-bada-ukasar-ukasar-urapon. Check: 8 + 2 + 1 = 11 ✅. Group ke group = base ka idea!

Q11. NCERT style Ek chaand ka chakra ≈ 29.5 din. Ek saal ke tally calendar mein kitne chakra?

Solution dekho

365 ÷ 29.5 ≈ 12.4, yaani lagbhag 12 chakra. Check: 12 × 29.5 = 354 din (ek din ki kaat se calendar) ✅

Q12. NCERT style Kyun 10-lakeer wala gate (|||||||||/) achha nahi?

Solution dekho

9 lakeerein ek nazar mein nahi dikhti (seema ~4). WHY: gate tabhi kaam ka jab woh khud ek nazar mein pehchaana jaaye.

Answer Key — charumam.com exclusive

🧠 HOTS (Sochne Wale Sawaal)

Q1. Gumulgal system mein (ukasar ×4 + urapon) − (ukasar ×2 + urapon) = ?

Solution dekho

urapon se urapon kata, 4 − 2 = ukasar-ukasar (4). Check: 9 − 5 = 4 ✅

Q2. Tally aur Gumulgal, dono mein 100 likhna ho to kaun chhota?

Solution dekho

Tally: 100 lakeer (20 gate). Gumulgal: 50 baar ukasar. Gate dekhne mein chhota, par dono lambe. WHY: dono mein sirf ek group size.

Q3. Agar insaan ek nazar mein 7 tak pehchaan paata, to gate kitne ka hota?

Solution dekho

Shayad 7–8 ka (6–7 khadi + tirchhi). WHY: gate ki lambaai dimaag ki seema se tay hoti hai.

Q4. Ek system 2 aur 5 dono group use karta hai: 5 = “haath”, 2 = “jodi”. 17 kaise?

Solution dekho

17 = haath + haath + haath + jodi = 15 + 2. Check: 3 × 5 + 2 ✅. Do group size = landmark numbers ki shuruaat (Post 3 — Roman Numerals Kaise Likhein?).

sirf charumam.com pe milenge!

🏆 Olympiad Corner

Q1. 5-gate tally mein 1 se 30 tak har number ek baar likho. Kul kitne poore gate banenge?

Solution dekho

Har number n ke liye ⌊n/5⌋ gate. Jod: 0×4 + 1×5 + 2×5 + 3×5 + 4×5 + 5×5 + 6 = 81 (n = 30 pe 6 gate).

Q2. Gumulgal mein 13 likhne ke liye kitne shabd?

Solution dekho

6 ukasar + 1 urapon = 7 shabd.

Q3. Ek haddi pe 7 gate + 4. Ek din chhoot gaya. Asli din?

Solution dekho

39 + 1 = 40.

Q4. 3-gate tally mein 50 ke kitne gate?

Solution dekho

50 = 16 × 3 + 2 → 16 gate + 2.

sirf charumam.com readers ke liye 🔐

💗 CharuMam Motivation

Ishaan ne socha tally bachchon ka khel hai. Par usi ki chhoti si trick (5 pe gate) se insaan ne aage chalkar base aur place value banaaye. Chhote idea, bade nateeje! 🌱

Agli baar 5-5 mein gino, to yaad rakhna: aap 20,000 saal purane ganitagyon ke saath baithe ho. 🦴

— 📌 charumam.com

🟢 Master Recap

💡 Chaabi: Har cheez ka ek nishaan (tally) ginti hai, par group banaana use tez aur saaf karta hai. Ek group ko ek naya naam ya chinh do: yahi aage chalkar “base” ka beej hai.
Shareer ke hisse bhi standard sequence ban sakte hain.
Tally = har cheez ek kaat; Lebombo (29 kaat, ~44,000 saal), Ishango (20,000–35,000 saal).
Ek nazar mein ~4 tak; isliye 5 pe gate.
Gumulgal: urapon 1, ukasar 2; 2-2 mein naam.
Group size 2, 5, 10, 20 alag logon ne chune.
Group ke group = base ka beej.

— charumam.com 🎯

👉 Aage Kya?

Ek hi group size se bade number lambe ho jaate hain. Romans ne kai “landmark” chinh banaye: I, V, X, L, C, D, M. Agle post mein: Roman numerals! 🏛️

← Pichla: Post 1 — Ginti Ki Shuruaat Kaise Hui?📚 Chapter 3 ke saare posts Agla: Post 3 — Roman Numerals Kaise Likhein? →

Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Cricket Ka Scorer Aur Ek Nazar Ka Khel

📖 Concept: Nishaan Se Group Tak

Step 1: Shareer se ginti

Step 2: Haddi pe nishaan (tally marks)

Step 3: Ek nazar ki seema

Step 4: 2-2 mein naam: Gumulgal

Step 5: Group size: 2, 5, 10, 20

🪜 Atak Gaye? Aise Socho

🔐 Deep Concept: Hum 5 Pe Gate Kyun Banaate Hain? (Grouping Ka Beej)

✏️ Solved Examples

🏠 Aaj Bhi Tally Aur Grouping

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

You may also like