Mental Addition: Todo aur Jodo
CharuMam ka Tod-Jod Formula: number ko gharon mein todo, bade ghar se jodna shuru karo, aur aakhir mein sab milao 🧩
🔥 Kahani: Gali cricket ka scoreboard
Sunday ko gali mein match tha. Rohan ne 46 run banaye aur Golu ne 38 run. Team ka total likhna tha, par scorer ki copy mein pen khatam ho gaya!
Rohan ne zameen pe lakdi se likhna shuru kiya: “6 + 8 = 14, 4 likho, 1 haasil… ruko, haasil kahan likhun?” Mitti mein sab mit gaya. 😅
Tab tak Priya ne aankhein band karke bola: “40 aur 30 = 70. 6 aur 8 = 14. 70 aur 14 = 84.” Teen chhote jod, aur jawaab taiyaar!
Golu ne poocha: “Tumne 46 aur 38 ko tod kyun diya?” Priya hansi: “Bade number ko ek saath pakadna mushkil hai. Tod do, toh har tukda aasan ho jaata hai.” Aaj wahi Todo aur Jodo wala dimaagi jod seekhenge.
✅ Prerequisite Checker
Yeh post samajhne ke liye itna aana chahiye:
- Number ko gharon mein todna: 46 = 40 + 6, 345 = 300 + 40 + 5 (MN-01: Place Value)
- 10 ke pakke dost: 7 + 3, 6 + 4, 8 + 2 (MN-08: Number Bonds)
- 20 tak ke chhote jod (jaise 6 + 8 = 14) aur 10-10 karke aage ginna: 46, 56, 66, 76
Bas! Agar tum 40 + 30 jaisa gol jod bina ungli ke kar lete ho, toh tum taiyaar ho. 🙂
📘 Concept: Todo, phir Jodo
46 asal mein 4 dahai aur 6 ikai hai, yaani 46 = 40 + 6. Isi tarah 38 = 30 + 8.
Kyun yeh zaroori hai? Kyunki “46” ek akela dabba nahi, do alag gharon ka mel hai (MN-01). Jab hum tukde dekh lete hain, toh bada jod chhote-chhote jodon mein badal jaata hai.
46 + 38 → dahai: 40 + 30 = 70. Ikai: 6 + 8 = 14. Ab milao: 70 + 14 = 84.
Kyun yeh sahi hai? Jod mein tukdon ka order aur group badalne se kul nahi badalta. 40 + 6 + 30 + 8 ko kisi bhi kram mein jodo, jawaab 84 hi aayega. Hum bas same ghar walon ko saath bitha rahe hain: dahai ke saath dahai, ikai ke saath ikai.
Paper pe hum ikai (daayein) se shuru karte hain. Par dimaag mein baayein se, yaani bade ghar se: pehle 40 + 30 = 70, phir ikai.
Kyun? Pehla jod (70) hi bata deta hai ki jawaab “70 ke upar kuch” hoga. Bada hissa pehle haath mein aa gaya, ab sirf chhota hissa jodna hai. Aur hum numbers bolte bhi baayein se hain: “chhiyaalis” mein pehle chalees aata hai.
46 ko poora rakho, sirf 38 ko todo: 30 aur 8. Ab chhalaang lagao: 46 + 30 = 76, phir 76 + 8 = 84.
Kyun yeh aur aasan lagta hai? Dimaag ko ek saath sirf ek number yaad rakhna padta hai: 76. Tareeka A mein 70 aur 14 dono yaad rakhne padte hain. Number line pe socho: 46 se 10-10 ki teen chhalaang (56, 66, 76), phir 8 aage.
76 + 8 mein 6 + 8 = 14, yaani 10 paar ho gaya. 76 ka agla gol number 80 hai, 6 ka dost 4. Toh 8 ko todo: 4 + 4. 76 + 4 = 80, phir 80 + 4 = 84.
Kyun? Gol number (80) tak pahunchna sabse aasan hai, kyunki uske baad ikai mein jo bacha woh seedha chipak jaata hai. Yeh wahi “pehle 10 banao” hai jo MN-08 mein seekha.
Tareeka A mein ikai ka jod 14 aaya. 14 = 10 + 4. Yeh 10 hi woh “1 haasil” hai jo paper pe dahai mein upar likhte hain. 70 + 14 karte hi woh 10 apne aap dahai mein jud gaya.
Kyun yeh achha hai? Haasil koi alag jaadu nahi. 10 ikai milke 1 dahai ban jaati hain, bas. Dimaagi jod mein haasil yaad rakhne ki zaroorat hi nahi padti, woh khud 14 ke andar baitha hai.
345 + 278 → saikda: 300 + 200 = 500. Dahai: 40 + 70 = 110. Ikai: 5 + 8 = 13. Milao: 500 + 110 = 610, 610 + 13 = 623.
Kyun 40 + 70 ko 110 likha, 11 nahi? Kyunki 4 dahai + 7 dahai = 11 dahai = 110. Ghar ki value saath rakhni hai. Agar sirf “11” yaad rakha toh 100 ka hisaab gayab ho jaayega.
345 lagbhag 350, 278 lagbhag 280. 350 + 280 = 630. Hamara jawaab 623, jo 630 ke bahut paas hai. ✅
Kyun? Dimaagi jod mein koi tukda chhoot jaaye toh jawaab andaaze se bahut door chala jaata hai. Ek second ka check badi galti pakad leta hai (andaaze ka tareeka MN-06 mein).
🎯 CharuMam ka Tod-Jod Formula
“Todo gharon mein, jodo bade ghar se. Ya ek ko poora rakho, doosre ki chhalaang lagao. Ikai 10 paar kare toh pakka dost bulao. Aakhir mein andaaze se milao.”
Scoreboard ka sach: 46 + 38 = 70 + 14 = 84. Priya ne bina pen ke sahi total likhwa diya! ✅
🖼️ Picture se samjho: 46 + 38 ke do raaste
Upar: Tareeka A, dono numbers gharon mein toote, dahai ke saath dahai aur ikai ke saath ikai. Neeche: Tareeka B, number line pe 46 se 10-10 ki teen chhalaang, phir pakke dost ki madad se 80 pe ruk ke 84.
✏️ Examples: aasan se mushkil tak
Example 1: 23 + 45 (ikai 10 paar nahi karti)
Dahai: 20 + 40 = 60. Ikai: 3 + 5 = 8. Milao: 60 + 8 = 68.
Kyun yeh sabse aasan hai? Ikai ka jod 8 hai, 10 se kam. Toh koi haasil nahi bana, 60 aur 8 seedhe “68” ban gaye. Aise sawaal 2 second mein dimaag mein ho jaate hain.
Example 2: 57 + 26 (dono tareeke)
Tareeka A: 50 + 20 = 70, 7 + 6 = 13, 70 + 13 = 83.
Tareeka B: 57 + 20 = 77. Ab 6 jodna hai: 77 ka agla gol number 80 (7 ka dost 3), toh 6 = 3 + 3. 77 + 3 = 80, 80 + 3 = 83.
Kyun dono same? Dono mein bas tukdon ka kram alag hai: A mein pehle dahai-dahai, B mein pehle poora 57. Jod mein kram badalne se kul nahi badalta, isliye jo tareeka tumhe aasan lage wahi chuno.
Example 3: 68 + 75 (jawaab 100 paar)
Dahai: 60 + 70 = 130. Ikai: 8 + 5 = 13. Milao: 130 + 13 = 143.
Andaaza: 70 + 80 = 150, aur 143 uske paas hai ✅
Kyun 60 + 70 = 130? Kyunki 6 dahai + 7 dahai = 13 dahai, aur 10 dahai = 100. Toh 13 dahai = 100 + 30 = 130. Ghar ki value saath rakhi, isliye 100 paar karna bhi aasan raha.
Example 4: Dukaan ka bill ₹249 + ₹186
Saikda: 200 + 100 = 300. Dahai: 40 + 80 = 120. Ikai: 9 + 6 = 15.
Milao: 300 + 120 = 420, 420 + 15 = ₹435. Andaaza: 250 + 190 = 440 ✅
Kyun teen tukde? 3-digit number mein teen ghar hain, toh teen chhote jod. Har jod ek “gol” jod hai jo dimaag mein aaram se ho jaata hai. Aakhir mein sirf 300, 120, 15 ko milana hai.
🧮 Khud karke dekho: CharuMam Tod-Jod Machine
💡 0 se 9999 tak ke do poore number daalo aur tareeka chuno. Machine dikhayegi ki number kaise toote, kaun sa tukda kis se juda, aur Tareeka B mein number line pe chhalaang kaise lagi. 46 + 38 ke baad 345 + 278 aur 68 + 75 try karo!
📕 Textbook yeh nahi batata
1. Paper ka tareeka aur dimaag ka tareeka ulte chalte hain, aur dono sahi hain. Column method mein ikai se shuru karte hain taaki haasil upar likh sakein. Dimaag mein bade ghar se shuru karna behtar hai, kyunki bada hissa pehle mil jaata hai. Jawaab dono ka same, kyunki jod mein tukdon ka kram badalne se kul nahi badalta.
2. Baayein se jodne mein andaaza muft milta hai. 345 + 278 mein pehla kadam (300 + 200 = 500) sunte hi pata chal gaya ki jawaab 500 se upar aur 700 se neeche hai. Exam mein MCQ ke galat options yahin kat jaate hain, poora jod karne se pehle hi.
3. Ek hi number ko alag-alag tareeke se tod sakte ho. 38 = 30 + 8 bhi hai, aur 38 = 34 + 4 bhi. 46 + 38 mein agar 38 ko 34 + 4 todo, toh 46 + 4 = 50 (pakka dost!), aur 50 + 34 = 84. Todne ka koi ek “sahi” tareeka nahi; jo tukde tumhare kaam aayein, wahi sahi.
🧠 Bachche yahan galti karte hain
❌ Galti 1: Tukdon ke jawaab ko paas-paas likh dena: 46 + 38 → “7 aur 14, toh 714”.
Yeh galat kyun hai? Dahai ka jod 4 + 3 = 7 dahai hai, yaani 70. Ikai ka jod 14 hai. 70 aur 14 ko jodna hai, paas-paas chipkana nahi: 70 + 14 = 84. Andaaza bhi bata deta: 50 + 40 = 90, toh 714 ho hi nahi sakta.
❌ Galti 2: Chhalaang mein ghar bhool jaana: 46 + 38 mein “pehle 3 jodo” karke 46 + 3 = 49.
Kyun galat? 38 ka 3 asal mein 3 dahai = 30 hai, 3 nahi. Sahi chhalaang 46 + 30 = 76. Tukda todte waqt uski ghar wali value saath le jao (MN-01 yaad karo).
❌ Galti 3: Koi tukda chhod dena: 345 + 278 → 500 + 110 = 610, aur ikai ka 13 bhool gaye.
Kyun galat? Har ghar ka tukda jodna zaroori hai. 3 ghar the, toh 3 tukde: 500, 110 aur 13. Sahi jawaab 623. Shuru mein hi gin lo ki kitne tukde hain, aur aakhir mein check karo ki sab jud gaye.
🌍 Real Life mein kahan?
🛒 Dukaan ka bill: Doodh ₹68 aur bread ₹45. 60 + 40 = 100, 8 + 5 = 13. Kul ₹113. Paise dene se pehle hi dimaag mein total pata.
🏏 Cricket: Pehli innings 156, doosri 127. 100 + 100 = 200, 50 + 20 = 70, 6 + 7 = 13. Kul 283 run. Commentator bhi aise hi jodta hai.
📝 Report card: Maths mein 78, Science mein 85. 70 + 80 = 150, 8 + 5 = 13. Dono milake 163 marks.
📱 Mobile data: Subah 350 MB video dekhi, shaam ko 275 MB. 300 + 200 = 500, 50 + 70 = 120, 0 + 5 = 5. Kul 625 MB. Pack khatam hone se pehle hisaab tumhare paas!
⏰ Dhyaan: Time jodte waqt 60 minute = 1 ghanta hota hai. 40 min + 35 min = 75 min = 1 ghanta 15 min. Wahan 10 ke gharon wala jod seedha nahi chalta. Time ki yeh baat MN-44 mein.
⚖️ Kab use karein, kab nahi
| ✅ Tod-Jod use karo jab… | ⚠️ Dhyaan rakho jab… |
|---|---|
| 2 ya 3 digit ke do number jodne ho (bill, score, marks) | Number bahut lambe ho (5-6 digit) ya bahut saare ho: tab paper ka column method zyada bharosemand hai |
| Tareeka A: jab dono numbers ke ghar saaf-saaf dikhein (23 + 45) | Tukdon ko jodna hai, paas-paas likhna nahi (70 aur 14 → 84, 714 nahi) |
| Tareeka B: jab ek number poora yaad rakhna aasan ho (46 + 30 + 8) | Time ka jod: 60 minute pe ghanta badalta hai, 100 pe nahi |
| ❌ Kabhi nahi: tukde ki ghar wali value bhool jaana (38 ka 3 matlab 30), ya aakhir mein andaaze se check na karna. | |
📝 Self-Check Quiz
Q1. 34 + 25 = ? (a) 59 (b) 69 (c) 509 (d) 49
✅ (a) 59: dahai 30 + 20 = 50, ikai 4 + 5 = 9, milake 50 + 9 = 59.
(b) galat: ikai ka jod 9 hai, 10 se kam, toh koi haasil nahi bana. 10 extra kahan se aaya?
(c) galat: 50 aur 9 ko paas-paas likh diya (Galti 1). 50 + 9 = 59 hota hai.
(d) galat: dahai 30 + 20 = 50 hai, 40 nahi. 10 kam reh gaya.
Q2. 47 + 36 ko Ghar-Ghar tareeke se karo. Sahi kaunsa? (a) 70 + 13 = 83 (b) 70 aur 13, toh 7013 (c) 7 + 13 = 20 (d) 70 + 13 = 73
✅ (a): dahai 40 + 30 = 70, ikai 7 + 6 = 13. 70 + 13 = 83.
(b) galat: tukdon ko jodna tha, paas-paas likhna nahi. Andaaza 50 + 40 = 90, toh 7013 bilkul bekaar.
(c) galat: 4 dahai + 3 dahai = 7 dahai = 70, sirf 7 nahi. Ghar ki value bhool gaye.
(d) galat: 13 mein se sirf 3 joda, 10 bhool gaye. 70 + 13 = 83, 73 nahi.
Q3. 58 + 27 ko “Ek Poora, Doosra Todo” se karo. Sahi kaunsa? (a) 58 + 20 = 78, 78 + 7 = 85 (b) 58 + 2 = 60, 60 + 7 = 67 (c) 58 + 20 = 78, 78 + 2 = 80 (d) 50 + 20 + 8 = 78
✅ (a): 27 = 20 + 7. Pehle 58 + 20 = 78, phir 78 + 7 = 85.
(b) galat: 27 ka 2 asal mein 20 hai (Galti 2). 2 jodne se 20 ki jagah sirf 2 juda.
(c) galat: 7 mein se sirf 2 joda (80 tak), baaki 5 bhool gaye. 80 + 5 = 85 tak jaana tha.
(d) galat: 27 ka 7 chhoot gaya (Galti 3). 78 + 7 = 85.
Q4. 256 + 137 = ? (a) 393 (b) 383 (c) 3813 (d) 493
✅ (a) 393: saikda 200 + 100 = 300, dahai 50 + 30 = 80, ikai 6 + 7 = 13. 300 + 80 + 13 = 393.
(b) galat: ikai ke 13 mein se sirf 3 joda, 10 bhool gaye.
(c) galat: 3, 8 aur 13 ko paas-paas likh diya. Tukde jodne the: 300 + 80 + 13.
(d) galat: saikda 200 + 100 = 300 hai, 400 nahi. 100 extra juda.
Q5. Priya ke paas ₹68 hain aur Golu ke paas ₹57. Dono milake kitne? (a) ₹115 (b) ₹125 (c) ₹1115 (d) ₹135
✅ (b) ₹125: dahai 60 + 50 = 110, ikai 8 + 7 = 15. 110 + 15 = 125.
(a) galat: ikai ke 15 mein se 10 bhool gaye, sirf 5 joda.
(c) galat: dahai ke digit 6 + 5 = 11 aur ikai 8 + 7 = 15 ko paas-paas likh diya (Galti 1).
(d) galat: 110 + 15 = 125 hota hai, 135 mein 10 extra jud gaya.
💪 Practice Zone
Har sawaal mein pehle number todo, phir jodo, aur aakhir mein andaaze se milao.
- 32 + 46 = ?
- 25 + 38 = ?
- 49 + 36 = ? (Tareeka B se, pakka dost bulao)
- 67 + 58 = ?
- 120 + 75 = ?
- 234 + 152 = ?
- 368 + 245 = ?
- Bill: ₹145 + ₹78 + ₹55 = ? (pehle pakke dost wali jodi dhundho)
Answer Key (click karo)
1) 30 + 40 = 70, 2 + 6 = 8 → 78 · 2) 20 + 30 = 50, 5 + 8 = 13 → 63 · 3) 49 + 30 = 79, 79 + 1 = 80, 80 + 5 = 85 · 4) 60 + 50 = 110, 7 + 8 = 15 → 125 · 5) 100 + 0 = 100, 20 + 70 = 90, 0 + 5 = 5 → 195 · 6) 200 + 100 = 300, 30 + 50 = 80, 4 + 2 = 6 → 386 · 7) 300 + 200 = 500, 60 + 40 = 100, 8 + 5 = 13 → 613 · 8) ₹145 + ₹55 = ₹200 (ikai 5 + 5 = 10, dahai 4 + 5 = 9, pakke dost!), phir 200 + 78 = ₹278
Answer Key — charumam.com exclusive
🚀 Challenge (HOTS)
Q1. Rohan kehta hai: “Do 2-digit numbers jodne pe kabhi-kabhi jawaab 200 ya usse zyada aa sakta hai.” Kya Rohan sahi hai? Ghar-Ghar tareeke se socho.
Solution
Nahi, Rohan galat hai. 2-digit number ki dahai zyada se zyada 9 (yaani 90) aur ikai zyada se zyada 9 hoti hai.
Dahai ka jod zyada se zyada 90 + 90 = 180. Ikai ka jod zyada se zyada 9 + 9 = 18.
Kul zyada se zyada 180 + 18 = 198 (yaani 99 + 99). Toh jawaab hamesha 200 se kam rahega.
Kyun yeh kaam ka hai? Ikai ka jod kabhi 20 tak nahi pahunchta, isliye ikai se dahai mein zyada se zyada ek hi haasil (10) jaata hai. Yeh samajh ho toh 2-digit jod ka jawaab 3-4 digit ka aaye, toh turant pata chal jaata hai ki galti hui.
Q2. Golu ke paas do 2-digit numbers hain jinka jod 100 hai. Dono ki dahai ke digit jodo toh 9 aate hain. Dono ki ikai ka jod kitna hoga? Aur agar dahai ke digit ka jod 8 hota, toh?
Solution
Ghar-Ghar socho: kul = (dahai ka jod) + (ikai ka jod). Dahai ke digit 9 matlab dahai ka jod 90. Toh 90 + (ikai ka jod) = 100, yaani ikai ka jod 10. Jaise 37 + 63: 30 + 60 = 90, 7 + 3 = 10.
Agar dahai ke digit 8 hote (80), toh ikai ka jod 20 chahiye hota. Par do ikai ka jod zyada se zyada 9 + 9 = 18 hai. Isliye aisa ho hi nahi sakta.
Kyun yeh achha hai? Yahi wajah hai ki MN-08 mein 100 ke dost ki dahai 9 tak aur ikai 10 tak jaati thi. Tod-Jod ne us rule ka kyun bhi khol diya.
❓ FAQ
Dimaag mein baayein se aur paper pe daayein se kyun jodte hain?
Paper pe daayein se isliye, taaki ikai ka haasil dahai ke upar likh sakein aur kuch mitana na pade. Dimaag mein likhne ki jagah nahi hoti, toh bada hissa pehle pakad lena behtar hai: 345 + 278 mein “500 ke upar” pehle hi pata chal jaata hai. Jod mein kram se fark nahi padta, isliye dono tareeke same jawaab dete hain.
Number todne se jawaab badal kyun nahi jaata?
Kyunki todna sirf likhne ka tareeka badalna hai, maatra nahi. 46 rupaye ko ₹40 ke note aur ₹6 ke sikke mein rakho, paise utne hi rahenge. Aur jodte waqt order ya group badalne se kul nahi badalta, isliye tukdon ko kisi bhi kram mein jodo.
Dimaagi jod mein haasil (carry) kyun nahi dikhta?
Dikhta hai, bas chupke se! 6 + 8 = 14 mein 14 = 10 + 4. Woh 10 hi haasil hai. Jab hum 70 + 14 karte hain, woh 10 apne aap dahai mein jud jaata hai. Isliye alag se “1 haasil” yaad rakhne ki zaroorat nahi padti.
Calculator hai toh dimaagi jod kyun seekhein?
Kyunki calculator tab hi kaam ka hai jab tumhe pata ho ki jawaab lagbhag kitna hona chahiye. Ek button galat dabaa toh 345 + 278 ka jawaab 3,023 aa sakta hai, aur dimaagi jod wala turant pakad lega ki yeh 600 ke aas-paas hona chahiye tha. Plus dukaan, cricket aur bill mein calculator nikaalne ka time hi kahan hota hai! 🙂
🔁 Recap
- Har number gharon ka mel hai: 46 = 40 + 6
- Tareeka A (Ghar-Ghar): dahai se dahai, ikai se ikai, phir milao: 46 + 38 = 70 + 14 = 84
- Tareeka B (Ek Poora, Doosra Todo): 46 + 30 = 76, 76 + 8 = 84
- Dimaag mein bade ghar se shuru karo; bada hissa pehle haath mein
- Ikai 10 paar kare toh pakka dost: 76 + 8 = 76 + 4 + 4 = 84
- Haasil = ikai ke jod ka 10. Tukde jodo, paas-paas mat likho, aur andaaze se check karo
💖 CharuMam Motivation
46 + 38 ek saath dekho toh thoda bhaari lagta hai. Par todte hi woh 40 + 30 aur 6 + 8 ban jaata hai, jo tum bachpan se jaante ho. Mushkil sawaal asal mein kai aasan sawaalon ka jhund hota hai. 🙂
Zindagi mein bhi aisa hi hai, beta. Poora syllabus ek saath dekhoge toh darr lagega. Use chapter mein todo, chapter ko topic mein, aur roz ek tukda jodo. Ek din peeche mudke dekhoge toh poora jod taiyaar milega. Bas Priya ki tarah yaad rakhna: koi tukda chhootna nahi chahiye! 🌱
— CharuMam
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