Number Bonds: 10 aur 100 ke jode
CharuMam ka Pakka-Dost Formula: har number ka ek pakka dost hota hai jo use poora 10 ya 100 bana deta hai 🤝
🔥 Kahani: Sharma uncle ka chhutta
School ke baad Golu, Rohan aur Priya Sharma uncle ki dukaan pe ruke. Golu ne chips aur toffee li, bill bana ₹37. Golu ne ₹100 ka note diya.
Rohan ne turant copy nikali: “100 − 37… 0 mein se 7 nahi jaata, udhaar lo… ruko, jawaab 73 aaya!” Rohan ko laga uncle kam paise denge. 🤔
Par Sharma uncle ne copy-pen kuch nahi uthaya. Sikke rakhte gaye aur bolte gaye: “37… aur 3 = 40. 40… aur 60 = 100.” Unhone ₹3 + ₹60 = ₹63 Golu ke haath mein rakh diye. Do second mein kaam khatam!
Priya ne Rohan ka 73 check kiya: “37 + 73 = 110 hota hai, 100 nahi. Tumne 10 rupaye zyada maang liye the!” 😅
Uncle hanse: “Beta, 37 ka 100 wala dost 63 hai. Jo yeh dost pehchaanta hai, use udhaar lene ki zaroorat hi nahi.” Aaj wahi pakke dost (Number Bonds) samjhenge.
✅ Prerequisite Checker
Yeh post samajhne ke liye itna aana chahiye:
- Ikai, dahai, saikda: 10 ikai milke 1 dahai, 10 dahai milke 1 saikda (MN-01: Place Value)
- 20 tak ke chhote jod-ghatav (jaise 7 + 5, 13 − 6)
- Ginti aage badhana: 37, 38, 39, 40… aur 10-10 karke: 40, 50, 60…
Bas! Agar tum ungliyon pe 10 tak gin sakte ho, toh yeh post tumhare liye hai. 🙂
📘 Concept: Pakke dost dhundho
Ek poora number (jaise 10) ko do hisson mein todo: 7 aur 3. Yeh do hisse aur woh poora number milke ek Number Bond banate hain: 7 + 3 = 10. Hum kahenge: 7 ka 10 wala pakka dost 3 hai.
Kyun “dost”? Kyunki 7 akela adhoora hai. 3 aate hi poora 10 ban jaata hai. Ek number ko poora karne wala ek hi dost hota hai: 7 ka 10 wala dost sirf 3 hai, koi aur nahi.
0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5. Bas itne hi! 6 + 4, 7 + 3 wagairah toh inhi ke ulte hain.
Kyun 10 itna khaas hai? Kyunki hamara number system 10 pe chalta hai (MN-01). Jaise hi ikai mein 10 poore hote hain, woh 1 dahai ban jaate hain. Toh jod-ghatav mein sabse zyada kaam aata hai yeh jaanna ki “10 banne mein kitna baaki hai”.
30 + 70 = 100, kyunki 3 dahai + 7 dahai = 10 dahai = 100. Isi tarah 40 + 60, 20 + 80, 90 + 10.
Kyun? 100 matlab 10 dahai. Toh 30 ka 100 wala dost dhundhna = 3 dahai ka 10 dahai wala dost dhundhna = 7 dahai = 70. Wahi purana 3 + 7 wala jodi, bas ghar badal gaya.
37 ka dost? Ikai: 7 ko 10 tak le jao, 3 chahiye. Dahai: 3 ko 10 tak nahi, sirf 9 tak le jao, 6 chahiye. Dost = 63. Check: 37 + 63 = 100 ✅
Dahai 9 tak hi kyun? Kyunki ikai wale 7 + 3 = 10 ikai milke khud ek dahai ban jaate hain! Woh 1 dahai upar chadh jaati hai. Toh dahai ko sirf 9 chahiye, 10th dahai ikai se aa jaayegi. 3 + 6 = 9 dahai, plus ikai se 1 dahai = 10 dahai = 100.
40 ka dost? Ikai 0 hai, toh ikai mein kuch nahi chahiye. Dahai ko poore 10 tak le jao: 4 + 6 = 10. Dost = 60.
Kyun yahan 9 nahi? Kyunki ikai mein koi 10 bana hi nahi, toh neeche se koi dahai upar nahi aayi. Ab dahai ko khud 10 tak jaana padega. Yaad rakho: “9 tak” sirf un gharon ke liye hai jinke neeche wale ghar ne 10 banake ek upar bheja ho.
37 se 100 tak jaana hai? Pehle agla gol number: 37 → 40 (+3). Phir 40 → 100 (+60). Kul 3 + 60 = 63.
Kyun yeh aasan hai? Pehla kadam 10 wala jodi hai (7 ka dost 3), doosra kadam 100 wala gol jodi (40 ka dost 60). Dono humein pehle se aate hain! Isliye 100 − 37 mein udhaar lene ki zaroorat hi nahi padi.
8 + 5? 8 ka 10 wala dost 2 hai. Toh 5 ko todo: 2 + 3. Ab 8 + 2 = 10, aur 10 + 3 = 13.
Kyun? 10 ke saath jodna sabse aasan hai (10 + 3 = 13 seedha dikhta hai). Dost ki madad se pehle ek “gol” 10 bana lo, baaki bacha hua seedha chipka do.
365 ka 1000 wala dost? Ikai 5 → 10 tak: 5. Dahai 6 → 9 tak: 3. Saikda 3 → 9 tak: 6. Dost = 635. Check: 365 + 635 = 1000 ✅
Kyun? Wahi kahani ek ghar aage: ikai 10 banake ek dahai upar bhejti hai, dahai 9 + 1 = 10 banake ek saikda upar bhejti hai, saikda 9 + 1 = 10 banake 1000 bana deta hai. Sabse aakhri (non-zero) digit 10 tak, baaki sab 9 tak.
🎯 CharuMam ka Pakka-Dost Formula
“10 ke 6 jode pakke yaad. 100 ka dost chahiye? Ikai 10 tak, baaki ghar 9 tak. Ikai 0 ho toh pehla non-zero ghar 10 tak. Phir jodke check karo: poora 100 aaya ya nahi.”
Chhutte ka sach: 37 ka dost 63 hai (ikai 7 + 3 = 10, dahai 3 + 6 = 9). Rohan ka 73 galat tha, Sharma uncle sahi! ✅
🖼️ Picture se samjho: 10 ka frame aur 100 ka grid
Baayein: 10 khaano ka frame, 7 neele aur 3 narangi. Daayein: 100 khaano ka grid (10 line, har line mein 10). 37 neele khaane aur 63 narangi. Dekho 4th line kaise 7 neele + 3 narangi se poori hui, isliye narangi ko poori lines sirf 6 chahiye, 7 nahi.
✏️ Examples: aasan se mushkil tak
Example 1: 6 ka 10 wala dost kaun?
6 + ? = 10. 6 se 10 tak gino: 7, 8, 9, 10, yaani 4 kadam. Dost = 4.
Kyun ise ratna faayde ka hai? 6 + 4 jaisa jodi baar-baar aata hai: 26 + 4 = 30, 46 + 4 = 50, 96 + 4 = 100. Ek jodi yaad, sau sawaal aasan.
Example 2: 100 − 58 bina udhaar ke
58 ka 100 wala dost dhundho. Ikai: 8 → 10, chahiye 2. Dahai: 5 → 9, chahiye 4. Dost = 42. Check: 58 + 42 = 100 ✅
Kyun ghatane ki jagah dost dhundha? “100 − 58” ka matlab hi hai “58 se 100 tak kitna aage jaana hai”. Woh doori hi 58 ka dost hai. Udhaar wala lamba tareeka bhi yahi jawaab deta hai, bas zyada kadam aur zyada galti ke mauke.
Example 3: 9 + 7 “pehle 10 banao” se
9 ka 10 wala dost 1 hai. Toh 7 ko todo: 1 + 6. Ab 9 + 1 = 10, aur 10 + 6 = 16.
Kyun yeh achha hai? Ungliyon pe 9 ke aage 7 ginne mein galti ho sakti hai. Par “10 aur 6” seedha 16 hai, kyunki 10 ke baad ikai mein jo likha hai wahi jud jaata hai (MN-01 ka ghar wala logic).
Example 4: ₹500 ka note, bill ₹263. Chhutta kitna?
Sharma uncle style mein aage gino: 263 → 270 (+7) → 300 (+30) → 500 (+200).
Chhutta = 7 + 30 + 200 = ₹237. Check: 263 + 237 = 500 ✅
Kyun teen kadam? Har kadam ek jaana-pehchaana jodi hai: 3 ka 10 wala dost 7, 7 dahai ka 10 dahai wala dost 3 dahai (30), aur 300 se 500 tak 200. Bade numbers mein bhi wahi chhote dost kaam kar rahe hain.
🧮 Khud karke dekho: CharuMam Pakka-Dost Machine
💡 Pehle 10, 100 ya 1000 chuno, phir 0 se lekar utne tak koi bhi poora number daalo. Machine dost batayegi, har ghar ka jodi dikhayegi (ikai 10 tak, baaki 9 tak), aur Sharma uncle wala “aage gino” tareeka bhi. 37 ke baad 40 aur 1000 ke saath 365 try karo!
📕 Textbook yeh nahi batata
1. Ghatana asal mein “dost dhundhna” hai. 100 − 37 ka matlab “37 mein se 37 hatao” bhi hai aur “37 se 100 tak kitna aage jaana hai” bhi. Dukaan wale doosra tareeka use karte hain kyunki usmein udhaar nahi lena padta. Is soch ko hum MN-11 mein aur gehrai se dekhenge.
2. “9-9-10” rule har 10, 100, 1000, 10,000 pe chalta hai. 10,000 − 2,486? Har digit ko 9 tak le jao, aakhri ko 10 tak: 2 → 7, 4 → 5, 8 → 1, 6 → 4. Jawaab 7,514. Check: 2,486 + 7,514 = 10,000 ✅. Ek line mein, bina ek bhi udhaar ke!
3. Dost pehchaanna “jodiyan dhundhne” ki aankh deta hai. 46 + 37 + 54 + 63? Line se mat jodo. 46 aur 54 dost hain (100), 37 aur 63 dost hain (100). Jawaab seedha 200. Jod mein order badalne se jawaab nahi badalta, isliye dost wale numbers ko paas laana bilkul sahi hai.
🧠 Bachche yahan galti karte hain
❌ Galti 1: Dono digits ko 10 tak le jaana: “37 ka 100 wala dost 73” (Rohan wali galti).
Yeh galat kyun hai? Ikai 7 + 3 = 10 ne pehle hi ek dahai upar bhej di. Ab agar dahai mein bhi 3 + 7 = 10 kar diya, toh kul 11 dahai = 110 ho gaya. Check karo: 37 + 73 = 110. Dahai sirf 9 tak jaayegi: dost 63.
❌ Galti 2: Ikai 0 hone pe bhi 9 wala rule: “40 ka dost 50” (dahai 4 + 5 = 9 kar diya).
Kyun galat? 40 + 50 = 90, 100 nahi. Ikai 0 hai, toh ikai ne koi dahai upar nahi bheji. Dahai ko khud 10 tak jaana hoga: 4 + 6 = 10, dost 60. “9 tak” sirf tab, jab neeche wale ghar ne 10 banaya ho.
❌ Galti 3: 1000 ke liye sab ghar 9 tak: “365 ka dost 634”.
Kyun galat? 365 + 634 = 999, ek kam reh gaya! Sab 9 tak le gaye toh 999 banta hai. Aakhri ghar (ikai 5) ko 10 tak le jaana tha: 5 + 5 = 10. Sahi dost 635. Hamesha jodke check karo.
🌍 Real Life mein kahan?
🛒 Dukaan ka chhutta: ₹100 ka note, saaman ₹72 ka. 72 ka dost? Ikai 2 → 10: 8, dahai 7 → 9: 2. Chhutta ₹28. Dukaan wale isi tarah aage gin ke paise lautate hain.
🏏 Cricket: Rohan 67 pe khel raha hai, century ke liye kitne run? 67 ka dost: 33. Commentator bhi turant bol deta hai “33 run door century se”.
📱 Mobile battery: Phone 28% pe hai. Poora 100% hone mein kitna baaki? 28 ka dost 72, yaani 72% charge aur chahiye.
📝 Exam ke marks: 100 mein se 86 aaye, toh kitne kate? 86 ka dost 14. Priya ko 14 marks ki galtiyan dhundhni hain.
⏰ Dhyaan: Ghadi mein ghanta 60 minute ka hota hai, 100 ka nahi. 4:45 se 5:00 tak 15 minute hain, 55 nahi! Wahan 60 ke dost chahiye (45 + 15 = 60). Time ki yeh baat MN-44 mein.
⚖️ Kab use karein, kab nahi
| ✅ Pakke dost use karo jab… | ⚠️ Dhyaan rakho jab… |
|---|---|
| 10, 100, 1000 jaise gol number mein se ghatana ho (chhutta, century, 100% battery) | Gol number 10, 100, 1000 na ho: 9-9-10 rule sirf inhi pe chalta hai. 500 − 263 jaise sawaal mein aage gino (Example 4) |
| Jod mein “pehle 10 banao”: 8 + 5 = 8 + 2 + 3 | Ikai 0 ho: tab us ghar ko chhodo aur pehla non-zero ghar 10 tak le jao (40 ka dost 60) |
| Bahut saare numbers jodne ho: pehle dost wali jodiyan dhundho (46 + 54, 37 + 63) | Time ka hisaab ho: ghanta 60 minute ka, wahan 100 wale dost nahi chalte |
| ❌ Kabhi nahi: 100 ke liye dono digits 10 tak le jaana (37 → 73), ya dost nikaal ke jodke check na karna. | |
📝 Self-Check Quiz
Q1. 6 ka 10 wala pakka dost kaun hai? (a) 5 (b) 4 (c) 6 (d) 14
✅ (b) 4: 6 + 4 = 10. 6 se aage gino: 7, 8, 9, 10, chaar kadam.
(a) galat: 6 + 5 = 11, ek zyada ho gaya.
(c) galat: 6 + 6 = 12. Number apna dost khud tabhi hota hai jab woh 10 ka aadha (5) ho.
(d) galat: 14 toh 6 aur 10 ko jodne se aata hai. Dost woh hai jo 6 mein judke 10 banaye.
Q2. 100 − 64 = ? (a) 46 (b) 36 (c) 44 (d) 34
✅ (b) 36: 64 ka dost. Ikai 4 → 10: 6. Dahai 6 → 9: 3. Check: 64 + 36 = 100.
(a) galat: dono digit 10 tak le gaye (Galti 1). 64 + 46 = 110.
(c) galat: 64 + 44 = 108. Ikai 4 + 4 = 8, 10 bana hi nahi.
(d) galat: 64 + 34 = 98. Ikai ko 10 ki jagah 8 tak le gaye, 2 kam reh gaye.
Q3. 1000 − 482 = ? (a) 518 (b) 528 (c) 618 (d) 517
✅ (a) 518: ikai 2 → 10: 8. Dahai 8 → 9: 1. Saikda 4 → 9: 5. Check: 482 + 518 = 1000.
(b) galat: dahai ko 10 tak le gaye. 482 + 528 = 1010.
(c) galat: saikda ko 10 tak le gaye. 482 + 618 = 1100.
(d) galat: ikai ko bhi sirf 9 tak le gaye (Galti 3). 482 + 517 = 999.
Q4. 7 + 6 ko “pehle 10 banao” tareeke se kaise karenge? (a) 7 + 3 + 3 = 13 (b) 7 + 3 + 6 = 16 (c) 7 + 3 + 4 = 14 (d) 7 + 6 − 3 = 10
✅ (a): 7 ka dost 3 hai, toh 6 ko 3 + 3 mein toda. 7 + 3 = 10, phir 10 + 3 = 13.
(b) galat: 3 toh 6 mein se liya tha, phir bhi poora 6 dobara jod diya. 3 extra jud gaya.
(c) galat: 6 ko 3 + 4 mein toda, par 3 + 4 = 7 hota hai, 6 nahi.
(d) galat: 10 banane ke liye 3 phenk diya! Number ghatane se sawaal hi badal gaya. 7 + 6 = 13, 10 nahi.
Q5. Cricket mein team ko 100 run chahiye, abhi 58 bane hain. Aur kitne chahiye? (a) 52 (b) 42 (c) 32 (d) 48
✅ (b) 42: 58 ka dost. Ikai 8 → 10: 2. Dahai 5 → 9: 4. Check: 58 + 42 = 100.
(a) galat: dahai ko 10 tak le gaye. 58 + 52 = 110.
(c) galat: 58 + 32 = 90, 10 run kam.
(d) galat: 58 + 48 = 106. Ikai 8 + 8 = 16, 10 nahi.
💪 Practice Zone
Har sawaal mein pehle pakka dost dhundho, phir jodke check karo.
- 3 ka 10 wala dost?
- 70 ka 100 wala dost?
- 23 ka 100 wala dost?
- 100 − 81 = ?
- 9 + 6 “pehle 10 banao” tareeke se karo
- 1000 − 247 = ?
- ₹200 ka note diya, bill ₹128. Chhutta kitna? (aage gino)
- 46 + 37 + 54 + 63 = ? (dost wali jodiyan dhundho)
Answer Key (click karo)
1) 7 (3 + 7 = 10) · 2) 30 (7 dahai + 3 dahai = 10 dahai) · 3) 77 (ikai 3 + 7 = 10, dahai 2 + 7 = 9; 23 + 77 = 100) · 4) 19 (ikai 1 + 9 = 10, dahai 8 + 1 = 9; 81 + 19 = 100) · 5) 9 + 1 + 5 = 10 + 5 = 15 · 6) 753 (2 + 7 = 9, 4 + 5 = 9, 7 + 3 = 10; 247 + 753 = 1000) · 7) 128 → 130 (+2) → 200 (+70), chhutta ₹72 · 8) (46 + 54) + (37 + 63) = 100 + 100 = 200
Answer Key — charumam.com exclusive
🚀 Challenge (HOTS)
Q1. Golu kehta hai: “Main aisa 2-digit number dhundh lunga jiska 100 wala dost uske ulte digits wala ho, jaise 37 ka dost 73 ho.” Kya aisa koi number hai?
Solution
Nahi, ek bhi nahi! Maan lo number ki dahai A aur ikai B hai (B zero nahi). Ulta number: dahai B, ikai A. Dost hone ke liye ikai ka jodi 10 chahiye: B + A = 10. Aur dahai ka jodi 9 chahiye: A + B = 9. Par A + B ek saath 10 aur 9 nahi ho sakta!
Aur agar B = 0 ho (jaise 40), toh ulta number “04” = 4 banta hai, jo 2-digit hi nahi. (40 ka dost toh 60 hai.)
Isliye Rohan ka 37 → 73 kabhi sahi ho hi nahi sakta: 37 + 73 = 110.
Kyun yeh kaam ka hai? 90 numbers ek-ek karke check karne ki zaroorat nahi padi. “Ikai 10, dahai 9” ke ek rule ne sab ek saath check kar diye.
Q2. Priya ne 1 se 99 tak saare numbers likhe. Usne 100 wale dost jodiyon mein milaye: 1 + 99, 2 + 98, 3 + 97… Kitni jodiyan banengi, kaunsa number akela bachega, aur 1 se 99 tak ka kul jod kitna hoga?
Solution
Jodiyan: 1 + 99, 2 + 98, … 49 + 51. Yeh 49 jodiyan hain, har ek = 100. Bacha 50, kyunki 50 ka dost 50 khud hai, aur use dobara nahi gin sakte.
Kul jod = 49 × 100 + 50 = 4,900 + 50 = 4,950.
Kyun yeh tez hai? 99 numbers line se jodne ki jagah sirf dost pehchaane. Isi chaal ko MN-12 (Gauss ki Chaal) mein aur aage le jaayenge.
❓ FAQ
10 ke jode hi sabse zaroori kyun hain?
Kyunki hamara number system 10 pe bana hai. Har baar jab ikai mein 10 poore hote hain, ek dahai ban jaati hai; 10 dahai se ek saikda. Jod-ghatav mein sabse zyada baar yahi sawaal aata hai: “agla 10 banne mein kitna baaki?” Jise 10 ke jode turant aate hain, uska har bada hisaab tez ho jaata hai.
100 ke dost mein dahai 9 tak hi kyun, 10 tak kyun nahi?
Kyunki ikai ka jodi (jaise 7 + 3 = 10) apne aap ek dahai bana deta hai, jo dahai ke ghar mein jud jaati hai. Agar dahai bhi 10 tak jaaye toh 9 + 1 ki jagah 10 + 1 = 11 dahai = 110 ho jaayega. Picture ka grid dekho: 4th line neele aur narangi milke poori karte hain, toh narangi ko poori lines sirf 6 chahiye.
Jode ratne chahiye ya samajhne chahiye?
Dono! 10 ke sirf 6 jode hain (0 + 10 se 5 + 5 tak), inhe itna pakka karo ki sochna na pade. Par 100 aur 1000 ke dost ratne nahi, banane hain, “ikai 10, baaki 9” se. Samajh hogi toh 365 ka dost bhi 5 second mein nikal aayega, bina koi table yaad kiye.
Kya kisi aur number (jaise 60 ya 500) ke bhi dost hote hain?
Haan, kisi bhi number ke. 45 ka 60 wala dost 15, 263 ka 500 wala dost 237. Bas “9-9-10” wala shortcut sirf 10, 100, 1000 jaise numbers pe chalta hai. Baaki jagah Sharma uncle ka tareeka lagao: agle gol number tak jao, phir target tak, aur kadam jod lo.
🔁 Recap
- Number Bond = poora number aur uske do hisse. 7 ka 10 wala pakka dost 3.
- 10 ke sirf 6 jode: 0 + 10, 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5
- 100 ka dost: ikai 10 tak, dahai 9 tak (37 → 63). Ikai 0 ho toh dahai 10 tak (40 → 60).
- 1000 ka dost: 9, 9, 10 (365 → 635)
- Ghatana = aage gino: 37 → 40 → 100. Jod = pehle 10 banao: 8 + 5 = 8 + 2 + 3
- Dost nikaalo toh jodke check zaroor karo: poora 100 aaya?
💖 CharuMam Motivation
7 akela adhoora lagta hai, 3 bhi. Par dono mile toh poora 10 ban gaye. Maths ke har number ka ek pakka dost hota hai jo use poora karta hai, aur woh dost uske jaisa nahi hota: 7 ka dost 3 hai, 7 nahi! 🙂
Zindagi mein bhi aisa hi hai, beta. Jo cheez tumhe nahi aati, woh shayad tumhare dost ko aati ho, aur jo usse nahi hoti, woh tum kar lete ho. Alag hona kamzori nahi, ek doosre ko poora karne ki taakat hai. Aur Rohan ki tarah galti ho jaaye, toh Priya ki tarah check karna seekho: jodke dekho, poora 100 bana ya nahi. 🌱
— CharuMam
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