Ghatana = Kitna aage jaana hai
CharuMam ka Aage-Badho Formula: chhote number se chalna shuru karo, gol stations pe ruko, aur saari chhalaangein jod do 🚶♀️
🔥 Kahani: Sharma Uncle ka ulta hisaab
Golu ki mummy ne ₹500 ka note diya aur kaha, “Sharma Uncle se saamaan le aao.” Bill bana ₹368. Golu ne copy nikaali aur likhne laga: “500 − 368… 0 mein se 8 nahi jaata, udhaar lo… par agla bhi 0 hai… 😵”
Tab tak Uncle ne change dena shuru kar diya. Har note rakhte hue bolte gaye: “368… yeh ₹2, ho gaye 370. Yeh ₹30, ho gaye 400. Yeh ₹100, ho gaye 500. Lo beta, ₹132.”
Golu hairaan: “Uncle, aapne toh ghataya hi nahi, aap toh jodte ja rahe the!” Uncle muskuraye: “Beta, 368 se 500 tak kitna aage jaana hai, wahi toh change hai.”
Shaam ko Rohan ne number line pe dikhaya ki 368 se 500 tak ki doori sach mein 132 hai. Aur Priya boli: “Matlab ghatav ka ek doosra roop bhi hai: kitna aage jaana hai?“ Aaj yahi seekhenge.
✅ Prerequisite Checker
Yeh post samajhne ke liye itna aana chahiye:
- Number line pe aage-peeche chalna aur do points ke beech doori dekhna (MN-04: Number Line)
- Kisi number se agla gol number kitna door hai: 47 se 50 tak 3, 368 se 400 tak 32 (MN-08: Number Bonds)
- Chhote-chhote tukde jodna: 3 + 30 + 2 = 35 (MN-09: Mental Addition)
- Gol number ke saath kaam karna aur hisaab barabar karna (MN-10: Compensation)
Bas! Agar tum bata sakte ho ki 47 se 50 tak kitna hai aur 50 se 80 tak kitna, toh tum taiyaar ho. 🙂
📘 Concept: Ghatav ko “doori” ki tarah dekho
82 − 47 ko do tarah padh sakte ho: (i) Le jaana: 82 cheezon mein se 47 hata do, kitni bachi? (ii) Farak / doori: 47 se 82 tak kitna aage jaana padega?
Kyun dono ka jawaab same? Agar 47 mein kuch (?) jodne se 82 banta hai, toh wahi “?” 82 aur 47 ka farak hai. 47 + ? = 82 aur 82 − 47 = ? ek hi rishte ko do taraf se dekhna hai. Jod aur ghatav ek hi sikke ke do pehlu hain.
Ab hum ghata nahi rahe, aage chal rahe hain. Number line pe 47 pe khade ho jao, aur 82 tak pahunchna hai.
Kyun yeh aasan lagta hai? Jodna dimaag ko ghatane se zyada aasan lagta hai, kyunki hum bachpan se aage ginte aaye hain: 1, 2, 3… Ulta ginna (82, 81, 80…) mein dimaag jaldi thakta hai.
47 ke baad pehla gol number (dahai) 50 hai. 47 se 50 tak = 3.
Kyun pehle gol number? Kyunki gol number (50) se aage badhna sabse aasan hai: ikai 0 hai, toh agli chhalaang sirf dahai mein hogi. Aur 47 se 50 tak ka 3 humein Number Bonds se pata hai (7 + 3 = 10).
50 se 80 tak = 30 (5 dahai se 8 dahai, yaani 3 dahai).
Kyun 80 pe ruke, 90 pe nahi? Kyunki target 82 hai. 90 toh 82 se aage nikal jaata. Hamesha woh sabse bada gol station chuno jo target se aage na ho.
80 se 82 tak = 2.
Kyun itna aasan? 80 gol hai, toh 82 tak bas ikai ka 2 bacha. Koi udhaar, koi haasil nahi.
3 + 30 + 2 = 35. Toh 82 − 47 = 35. Check: 47 + 35 = 82 ✅
Kyun jodte hain? Poori doori (47 se 82) teen tukdon mein bati hai. Tukde jodo toh poori doori milti hai, jaise ghar se school ka raasta: ghar se chauraha + chauraha se mandir + mandir se school.
503 − 278: 278 → 280 (2) → 300 (20) → 500 (200) → 503 (3). Kul: 2 + 20 + 200 + 3 = 225.
Kyun yahan best? Column mein 503 − 278 karo toh 3 mein se 8, phir 0 se udhaar, phir 5 se udhaar… zero ke paar udhaar lena hi sabse badi galti ki jagah hai (iski poori baat MN-13 mein). Aage-Badho mein koi udhaar nahi, sirf gol stations.
82 − 47 mein dono ko 3 aage badha do: 85 − 50 = 35. Same jawaab!
Kyun? Socho Rohan 47 number ke ghar pe hai aur Priya 82 pe. Dono saath-saath 3 kadam aage chalein, toh beech ki doori nahi badlegi. Dhyaan do: jod mein (MN-10) ek se lekar doosre ko dete the. Ghatav mein dono mein same jodo (ya dono se same ghatao).
🎯 CharuMam ka Aage-Badho Formula
“Chhote number pe khade ho jao. Pehle agle gol station tak, phir badi gol chhalaang, phir target tak. Saari chhalaangein jodo, wahi jawaab.”
Dukaan ka sach: 500 − 368 → 368 → 370 (2) → 400 (30) → 500 (100) = ₹132. Sharma Uncle bilkul sahi the! ✅
🖼️ Picture se samjho: 47 se 82 tak teen chhalaang
Upar: ghatav ka sawaal kaise jod ka sawaal ban jaata hai. Neeche: number line pe 47 se chalo. Chhoti chhalaang 50 tak (+3), badi chhalaang 80 tak (+30), aur aakhri chhoti chhalaang 82 tak (+2). Teeno jodo: 35.
✏️ Examples: aasan se mushkil tak
Example 1: 62 − 38
38 se chalo: 38 → 40 (2) → 60 (20) → 62 (2). Kul: 2 + 20 + 2 = 24. Check: 38 + 24 = 62 ✅
Kyun 60 pe ruke? Agla gol station 70 hota, par woh 62 se aage nikal jaata. Isliye 60 tak dahai ki chhalaang, phir baaki 2.
Example 2: 300 − 176
176 → 180 (4) → 200 (20) → 300 (100). Kul: 4 + 20 + 100 = 124.
Kyun 180 ke baad seedha 200? Kyunki 200 saikde ka gol station hai. Pehle dahai pura karo (180), phir saikda pura karo (200), phir saikde-saikde ki chhalaang. Column se karte toh do zero ke paar udhaar lena padta.
Example 3: 703 − 458
458 → 460 (2) → 500 (40) → 700 (200) → 703 (3). Kul: 2 + 40 + 200 + 3 = 245.
Andaaza: 700 − 450 = 250, aur 245 uske paas hai ✅
Kyun chhalaangein alag likhi? Chaar tukde dimaag mein yaad rakhna mushkil hai. Har chhalaang chhoti line mein likh lo, phir aakhir mein jodo. Pen-paper pe bhi yeh column se tez aur safe hai.
Example 4: Priya ki Dadi 1958 mein paida hui. 2026 mein unki umar?
1958 → 1960 (2) → 2000 (40) → 2026 (26). Kul: 2 + 40 + 26 = 68 saal (agar is saal ka janmdin aa chuka ho).
Kyun yahan Aage-Badho perfect hai? Umar ka sawaal asal mein “1958 se 2026 tak kitne saal aage?” hai. Saal ek line pe chalte hain, toh doori wala tareeka bilkul natural hai. 2026 − 1958 ko column se karna (6 mein se 8, 2 mein se 5, 0 mein se 9…) kaafi jhanjhat hai.
🧮 Khud karke dekho: CharuMam Aage-Badho Machine
💡 0 se 9,999 tak ke do poore number daalo (pehla bada, doosra chhota). Machine chhote number se chalegi, gol stations pe rukegi, aur har chhalaang dikhayegi. 82 − 47 ke baad 500 − 368, 703 − 458 aur 2026 − 1958 try karo!
📕 Textbook yeh nahi batata
1. Dukaandaar sadiyon se yahi karte aaye hain. Jab calculator aur UPI nahi the, tab dukaandaar change ginne ke liye ghatate nahi the, bill se note tak “aage gin ke” paise lautaate the: 368… 370… 400… 500. Is tareeke mein galti kam hoti hai, aur grahak bhi saath-saath check kar sakta hai.
2. Kab “le jaana” aur kab “aage jaana”? Jab dono number paas-paas hon, aage jaana jaadu hai: 1003 − 997 → 997 → 1000 (3) → 1003 (3) = 6. Column mein yahi sawaal do zero ke paar udhaar maangta hai! Par jab ghatane wala number bahut chhota ho, jaise 82 − 3, toh bas 3 peeche gin lo: 81, 80, 79. Sahi sawaal ke liye sahi tareeka.
3. Ghatav ka jawaab hamesha jod se check hota hai. 82 − 47 = 35 hai ya nahi? 47 + 35 karo. 82 aaya toh pakka sahi. Yeh 5 second ka check exam mein bahut marks bachata hai, kyunki ghatav mein galti jod se zyada hoti hai.
🧠 Bachche yahan galti karte hain
❌ Galti 1: Chhalaang ki jagah stations jod dena: 82 − 47 → “50 + 80 + 82 = 212”.
Yeh galat kyun hai? 50, 80, 82 toh ruke kahan (stations) hain, kitna chale nahi. Jodna hai chhalaangon ko: 3 + 30 + 2 = 35. Common sense check: 82 − 47 ka jawaab 82 se bada kaise ho sakta hai?
❌ Galti 2: Gol station target se aage nikal jaana: 62 − 38 → 38 → 40 (2) → 70 (30), “jawaab 32”.
Kyun galat? 70 toh 62 se aage hai, hum 8 zyada chal gaye. Sahi: 40 → 60 (20) → 62 (2), kul 2 + 20 + 2 = 24. Badi chhalaang hamesha target se pehle wale gol number tak lo.
❌ Galti 3: Ghatav mein jod wala balancing laga dena: 82 − 47 → 47 ko 3 diye aur 82 se 3 le liye → 79 − 50 = 29.
Kyun galat? Ek ko aage aur doosre ko peeche khiskaya, toh doori 6 se ghat gayi. Ghatav mein dono ko same taraf khiskao: 85 − 50 = 35. Yaad rakho: jod mein “ek se lo, doosre ko do”, ghatav mein “dono ko same do”.
🌍 Real Life mein kahan?
🛒 Change lena: Bill ₹368, note ₹500. 368 → 370 → 400 → 500: ₹2 + ₹30 + ₹100 = ₹132 wapas.
🏏 Cricket: Target 150, team 87 pe hai. 87 → 90 (3) → 150 (60). 63 run aur chahiye.
📱 Mobile battery: Phone 38% pe hai. 100% tak kitna charge baaki? 38 → 40 (2) → 100 (60) = 62%.
📚 Kitaab: Golu page 145 pe hai, kitaab 230 page ki hai. 145 → 150 (5) → 200 (50) → 230 (30) = 85 page aur.
🎂 Umar: Papa 1985 mein paida hue, Golu 2014 mein. Farak? 1985 → 1990 (5) → 2000 (10) → 2014 (14) = 29 saal.
⚖️ Kab use karein, kab nahi
| ✅ Aage-Badho use karo jab… | ⚠️ Dhyaan rakho / mat karo jab… |
|---|---|
| Bade number mein zero ho: 500 − 368, 1000 − 456, 2006 − 1997 | Ghatane wala number bahut chhota ho (82 − 3): bas peeche gin lo |
| Dono number paas-paas hon: 1003 − 997, 2010 − 1985 | Koi udhaar na lagta ho (86 − 23 = 63): har ghar seedha ghatao |
| Sawaal hi “kitna aur?”, “kitna farak?”, “kitna change?” ho | Chhalaangein yaad nahi reh rahi: dimaag mein mat rakho, likh lo |
| ❌ Kabhi nahi: stations (50, 80, 82) ko jod dena, ya gol station pe target se aage nikal jaana. | |
📝 Self-Check Quiz
Q1. 73 − 46 ko Aage-Badho se karo. Jawaab? (a) 29 (b) 27 (c) 34 (d) 193
✅ (b) 27: 46 → 50 (4) → 70 (20) → 73 (3). Kul 4 + 20 + 3 = 27. Check: 46 + 27 = 73 ✅
(a) galat: 46 se 50 tak 4 hai, 6 nahi. 6 toh 46 ki ikai hai. 6 + 20 + 3 = 29 ho gaya.
(c) galat: 50 se 80 tak chhalaang le li (30), jo 73 se aage hai (Galti 2). 4 + 30 = 34.
(d) galat: stations 50 + 70 + 73 jod diye (Galti 1). Jawaab 73 se bada ho hi nahi sakta.
Q2. 400 − 165 = ? (a) 365 (b) 235 (c) 230 (d) 245
✅ (b) 235: 165 → 170 (5) → 200 (30) → 400 (200). Kul 5 + 30 + 200 = 235.
(a) galat: column mein har ghar mein “bade mein se chhota” ghata diya (5 − 0, 6 − 0, 4 − 1). Udhaar wala ghatav aise nahi hota.
(c) galat: pehli chhalaang (165 se 170 = 5) bhool gaye: 30 + 200 = 230.
(d) galat: 170 se 200 tak 30 hai, 40 nahi. 5 + 40 + 200 = 245.
Q3. Inmein se kaunsa 82 − 47 ke barabar hai? (a) 79 − 50 (b) 85 − 44 (c) 85 − 50 (d) 80 − 50
✅ (c) 85 − 50: dono ko 3 aage khiskaya, doori same: 35.
(a) galat: ek ko peeche, ek ko aage khiskaya (Galti 3). 79 − 50 = 29.
(b) galat: 82 ko aage aur 47 ko peeche khiskaya, doori badh gayi: 85 − 44 = 41.
(d) galat: 82 ko 2 peeche aur 47 ko 3 aage khiskaya, alag-alag: 80 − 50 = 30.
Q4. Golu ne ₹1,000 ka note diya, bill ₹637 ka. Kitna change milega? (a) ₹363 (b) ₹373 (c) ₹463 (d) ₹360
✅ (a) ₹363: 637 → 640 (3) → 700 (60) → 1000 (300). Kul 3 + 60 + 300 = 363.
(b) galat: 640 se 700 tak 60 hai, 70 nahi. 3 + 70 + 300 = 373.
(c) galat: 700 se 1000 tak 300 hai, 400 nahi. 3 + 60 + 400 = 463.
(d) galat: pehli chhalaang (637 se 640 = 3) chhoot gayi: 60 + 300 = 360.
Q5. Kis sawaal mein Aage-Badho sabse kam faaydemand hai? (a) 1003 − 997 (b) 500 − 268 (c) 95 − 2 (d) ₹200 − ₹137 ka change
✅ (c) 95 − 2: sirf 2 ghatana hai. 2 se 95 tak chhalaangein lagane se achha hai seedha 2 peeche gin lo: 94, 93. Jawaab 93.
(a) galat: numbers paas-paas hain, Aage-Badho best: 997 → 1000 (3) → 1003 (3) = 6.
(b) galat: 500 mein zero hain, Aage-Badho bahut kaam ka: 268 → 270 (2) → 300 (30) → 500 (200) = 232.
(d) galat: change ginna toh Aage-Badho ka asli ghar hai: 137 → 140 (3) → 200 (60) = ₹63.
💪 Practice Zone
Har sawaal mein chhote number se chalo, gol stations likho, har chhalaang ke upar uski lambai likho, aur aakhir mein chhalaangein jodo.
- 52 − 27 = ?
- 91 − 64 = ?
- 100 − 58 = ?
- 300 − 147 = ?
- 605 − 389 = ?
- 1000 − 456 = ?
- 2010 − 1985 = ?
- Rohan ki team ka target 213 run hai, abhi score 148 hai. Kitne run aur chahiye?
Answer Key (click karo)
1) 27 → 30 → 50 → 52: 3 + 20 + 2 = 25 · 2) 64 → 70 → 90 → 91: 6 + 20 + 1 = 27 · 3) 58 → 60 → 100: 2 + 40 = 42 · 4) 147 → 150 → 200 → 300: 3 + 50 + 100 = 153 · 5) 389 → 390 → 400 → 600 → 605: 1 + 10 + 200 + 5 = 216 · 6) 456 → 460 → 500 → 1000: 4 + 40 + 500 = 544 · 7) 1985 → 1990 → 2000 → 2010: 5 + 10 + 10 = 25 · 8) 148 → 150 → 200 → 213: 2 + 50 + 13 = 65 run
Answer Key — charumam.com exclusive
🚀 Challenge (HOTS)
Q1. Priya ne ek number socha. Woh 47 se theek 35 door hai. Golu kehta hai, “Pakka 82 hai.” Kya sirf ek hi jawaab hai? Number line se socho.
Solution
Do jawaab ho sakte hain: 82 aur 12.
47 se 35 aage chalo: 47 + 35 = 82. Aur 47 se 35 peeche chalo: 47 − 35 = 12. Check: 82 − 47 = 35 aur 47 − 12 = 35 ✅
Kyun yeh important hai? Doori ki koi disha nahi hoti. “Kitna door?” ka jawaab hamesha positive hota hai, chahe aage jao ya peeche. Isliye farak nikalte waqt hamesha chhote number se bade ki taraf chalo.
Q2. 8,003 − 2,996 ko 30 second mein karo. Do tareeke se karke dikhao.
Solution
Tareeka 1 (Aage-Badho): 2996 → 3000 (4) → 8000 (5000) → 8003 (3). Kul 4 + 5000 + 3 = 5,007.
Tareeka 2 (dono ko saath khiskao): dono mein 4 jodo: 8007 − 3000 = 5,007.
Check: 2996 + 5007 = 8003 ✅
Kyun itna tez? 2,996 ek gol number (3,000) ke bilkul paas hai. Column mein yahi sawaal do zero ke paar udhaar maangta, aur galti ke chances bahut. Number ko dekh ke tareeka chuno, yahi number sense hai.
❓ FAQ
Ghatav ka sawaal jod se kyun kar rahe hain? Kya yeh cheating hai?
Bilkul nahi! Jod aur ghatav ek hi rishte ke do roop hain. 47 + 35 = 82 likho, toh usi se 82 − 47 = 35 aur 82 − 35 = 47 bhi nikal aate hain. Hum bas woh roop chun rahe hain jo dimaag ko aasan lage. Maths mein sahi raasta chunna hoshiyaari hai, cheating nahi. 🙂
Pehle agle gol number tak hi kyun jaate hain?
Kyunki gol number se aage badhna sabse aasan hai: 50 se 80, 300 se 700, sirf ek ghar badalta hai. Agar 47 se seedha 35 ki chhalaang lagane ki koshish karo, toh wahi purana haasil-udhaar wala kaam aa jaata hai. Gol station ek “rest stop” hai jahan se aage ka raasta saaf dikhta hai.
47 se 82 tak aur 82 se 47 tak doori same hai?
Haan, doori dono taraf 35 hi hai, jaise ghar se school aur school se ghar ka raasta. Par ghatav mein order maayne rakhta hai: 82 − 47 = 35, jabki 47 − 82 = −35 (negative, MN-04 yaad karo). Minus ka nishaan bas disha batata hai: peeche ki taraf.
Phir column wala ghatav (udhaar wala) kyun seekhte hain?
Woh bhi zaroori hai: bahut bade numbers ke liye, ya jab kaagaz pe saaf likhna ho. Par column method tab tak hi achha hai jab tak tumhe pata ho ki udhaar ka matlab kya hai. Aage-Badho tumhe ghatav ka matlab samjhata hai, aur jawaab check karne ka doosra raasta deta hai. Udhaar wale ghatav mein galti kyun hoti hai, yeh MN-13 mein dekhenge.
🔁 Recap
- Ghatav ke do matlab: le jaana aur kitna aage jaana hai (doori). Dono ka jawaab same
- 82 − 47 = ? ko socho: 47 + ? = 82
- Aage-Badho: chhote number se chalo → agla gol station → badi gol chhalaang → target. 47 → 50 → 80 → 82
- Jodna hai chhalaangon ko (3 + 30 + 2 = 35), stations ko nahi
- Badi chhalaang kabhi target se aage nahi jaani chahiye
- Ghatav mein dono numbers ko same khiskao toh farak same: 82 − 47 = 85 − 50
- Zero wale aur paas-paas ke numbers mein yeh tareeka sabse tez aur safe hai
💖 CharuMam Motivation
Golu ko 500 − 368 dekh ke darr laga, kyunki usne poora sawaal ek saath dekha. Sharma Uncle ne bas agla chhota station dekha: pehle 370, phir 400, phir 500. Har kadam aasan tha, aur saare kadam milke poora raasta ban gaya. 🙂
Zindagi mein bhi bade sapne door lagte hain, beta: board exam, sports team, ya koi nayi skill. Poori doori dekh ke ghabraao mat. Bas yeh poochho: “Mera agla gol station kaunsa hai?” Ek chapter, ek practice, ek din. Chhoti-chhoti chhalaangein jodte jao, aur ek din pata chalega ki tum target pe pahunch chuke ho! 🌱
— CharuMam
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