Hello friend!! Aaj ke lesson me hum aapko Rational numbers ke Operations ke baare me batane jaa rahe hai. Rational numbers ke 4 operations - Addition, Subtraction, Multiplication aur Division inn sabhi ko achhe se samjhayenge.
Rational numbers operations ke iss topic ko hum full details me sikhenge. Iss topic ke ek-ek point ke baare me hum aapko sikhayenge. Jissase aapko kahi aor jaane ki jarurat hi naa ho.
Rational numbers kya hai? Isski defination aur examples ke baare me hum pahle hi bata chuke hai. Agar aapko uss lesson ko padhna hai to nichey humne uss topic ka link diya hai. Aap chahe to padh sakte hai: Rrational numbers Defination with examples yaha padhe. To chaliye aaj ka lesson start karte hai:
Hum sabhi jaante hai ki, Rational numbers "parimey sankhya (परिमेय संख्या)", wo numbers hote hai jinko hum p/q ke rup me likh sakte hai. Jisme p aur q , dono integer hote hai aur q ki value zero nahi honi chahiye. Means q ≠ 0 .
Rational number p/q me hum p = numerator (Ansh) aur q = denominator (Har) kahte hai.
Example: 2/5, -3/7, 5/6 ... etc. ye sabhi parimey sankhyaye hai. Jisme 2, -3 aur 5 "Ansh" hai. Jabki 5, 7 aur 6 "Har" hai.
(2). Rational numbers ka Subtraction
(3). Rational numbers ka Multiplication
(4). Rational numbers ka Division
(i) Wo rational numbers, jinka denominator (Har) same ho.
(ii) Wo Rational numbers jinka denominator (Har) different (same nahi) ho.
(i) Wo Rational number jinka denominator (Har) same ho:
Example-1. 2/5 aur 1/5 ke "Har" same hai. Innka addition hum nichey step-by-step karte hai.
Solution: Hume 2/5 aur 1/5 ko add karna hai. Means,
⇒ 2 + 1
5 5
Step-1. Sabse pahle ek line khich kar uske nichey 5 likhe.
Jaise-:
5
Step-2. Ab 5 aur line ke uppar 2+1 likhe.
Jaise-: 2 + 1
5
Step-3. 2+1 = 3 likhkar uske niche 5 likhe. Bas ho gaya.
Jaise-: 2 + 1 = 3 Ans.
5 5
Example-2. Add 5/7 aur 4/7.
Solution-: 5/7 aur 4/7 ke Har = 7 same hai. To inka addition iss prakar se hoga.
5 + 4 = 5+4 = 9 Ans.
7 7 7 7
To ye tha unn rational number ka addition jinka denominator (har) same ho. Ab hum aapko batane jaa rahe hai unn rational number ka addition jinka denominator (har) different ho. To aayie issko bhi sikh lete hai:
(ii) Wo Rational number jinka denominator (Har) different (same nahi) ho:
Example-1. 7/9 aur 5/6 ke Har different (same nahi) hai. Innka addition hum nichey step-by-step karte hai.
Solution: Hume 7/9 aur 5/6 ko add karna hai. Means,
⇒ 7 + 5
9 6
Step-1. Sabse pahle denominator = 9 aur 6 ka L.C.M. nikale.
Jaise-: 2| 6, 9
3| 3, 9
3| 1, 3
| 1, 1
L.C.M. = 2×3×3 = 18
Step-2. Ab ek line khichkar uske niche L.C.M. = 18 likhe.
Jaise-:
18
Step-3. Ab 7/9 ke denominator 9 se L.C.M 18 ko divide karke. Bhagphal me numerator 7 se multiply kare. Issko note kare.
Jaise-: 18÷9 = 2
2×7 = 14
14 +
18
Step-4. Second Rational number 5/6 ke liye bhi same step-3 jaisa hi karenge.
Jaise-: 18÷6 = 3
3×5 = 15
14 + 15 = 29 Ans.
18 18
Example-2. 4/14 aur 3/8 Add kariye.
Solution-: Hume 4/14 aur 3/8 ko add karna hai. Jinke denominator different hai.
⇒ 4 + 3
14 8
Step-1. 14 aur 8 ka L.C.M. nikalenge.
2 | 14, 8
2 | 7, 4
2 | 7, 2
7 | 7, 1
| 1, 1
L.C.M. = 2×2×2×7 = 56
Step-2. 224+21 = 245 Ans.
56 56
(i). Wo Parimey sankhya jinka Har same ho.
(ii). Wo Parimey sankhya jinka Har different ho.
(i) Wo Parimey sankhya jinka Har same ho:
Jis tarah humne addition ke liye jo step ko follow kiya hai. Same wahi steps subtraction me bhi karna hai.
kewal ek change hoga. Addition me hum "plus(+)" ka use karte hai. Jabki subtraction me hum "minus (-)" ka use karenge.
Example: 12/17 me se 8/17 ko subtract kijiye.
Solution-: 12/17 aur 8/17 ke denominator same hai.
12 - 4 = 12 - 4 = 8 Ans.
17 17 17 17
(i) Wo Parimey sankhya jinka Har different (same nahi) ho:
Example: 5/8 aur 9/10 ko subtract kijiye.
Solution: 15/8 aur 9/10 ka denominator (Har) different (same nahi) hai. To isska solution iss prakar se hai:
⇒ 15 - 9
8 10
Step-1. 8 aur 10 ka L.C.M. nikalenge.
2 | 8, 10
2 | 4, 5
2 | 2, 5
5 | 1, 5
| 1, 1
L.C.M. = 2×2×2×5 = 40
Step-2. 75 - 36 = 39 Ans.
40 40
Example-1. -3/5 aur 7/8 ka multiply kijiye.
Solution: -3/5 aur 7/8 ka multiply hum iss prakar se kar sakte hai:
⇒ -3 × 7
5 8
⇒ -3 × 7
5 × 8
⇒ -21 Ans.
40
Agar aapko abhi bhi koi doubt hai to nichey diye steps ko follow kijiye:
Step-1. Dono Parimey sankhya ke numerator ka multiply kare.
Step-2. Dono Parimey sankhya ke denominator ka multiply kare.
Step-3. Denominator ke product ko numerator ke product se divide kare.
Example-2. 13/7 aur -6/15 ka multiply kijiye.
Solution: 13/7 aur 6/15 ka multiply hum iss prakar se kar sakte hai:
⇒ 13 × -6
7 15
⇒ 13 × (-6)
7 × 15
⇒ -78 Ans.
105
Kisi number (x) ka kisi other number (y) se divide karne ke liye hume number x ka multiply y ke reciprocal (ulta) 1/y se karna hota hai.
Means, x÷y = x×1/y
Example: 9/13 ko 5/7 se divide kijiye.
Solution: Hume 9/13 ko 5/7 se divide karna hai. Means,
⇒ 9 ÷ 5
13 7
Step-1. Sabse pahle 9/13 ko likhkar "÷" sign ki jagah "×" likhe. aur 5/7 ka reciprocal (ulta) 7/5 karke likhe.
Jaise-: 9 × 7
13 5
Step-2. Ab numerator 9 aur 7 ka aapas me multiply kare aur denominator 13 aur 5 ka aapas me multiply kare.
Jaise-: 9 × 7 = 63 Ans.
13×5 65
Ye bhi padhe-:
❒Natural numbers kya hai ? with example | Properties
❒Equilateral triangle (sambaahu tribhuj) ka area formula proof in hindi
❒Prove that medians of a triangle divides each other in the ratio 2:1
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Agar aapko aaj ka topic helpful laga ho to please ek share jarur kare.
Rational numbers operations ke iss topic ko hum full details me sikhenge. Iss topic ke ek-ek point ke baare me hum aapko sikhayenge. Jissase aapko kahi aor jaane ki jarurat hi naa ho.
Rational numbers kya hai? Isski defination aur examples ke baare me hum pahle hi bata chuke hai. Agar aapko uss lesson ko padhna hai to nichey humne uss topic ka link diya hai. Aap chahe to padh sakte hai: Rrational numbers Defination with examples yaha padhe. To chaliye aaj ka lesson start karte hai:
Hum sabhi jaante hai ki, Rational numbers "parimey sankhya (परिमेय संख्या)", wo numbers hote hai jinko hum p/q ke rup me likh sakte hai. Jisme p aur q , dono integer hote hai aur q ki value zero nahi honi chahiye. Means q ≠ 0 .
Rational number p/q me hum p = numerator (Ansh) aur q = denominator (Har) kahte hai.
Example: 2/5, -3/7, 5/6 ... etc. ye sabhi parimey sankhyaye hai. Jisme 2, -3 aur 5 "Ansh" hai. Jabki 5, 7 aur 6 "Har" hai.
Rational Numbers Operation | Full details in Hindi
Hum jaante hai ki, mathematic me 4 main operations hote hai- Addition, Subtraction, Multiplication and Division. To iss prakar se Rational numbers ke bhi 4 main operations nichey diya gaya hai-:
(1). Rational numbers ka Addition(2). Rational numbers ka Subtraction
(3). Rational numbers ka Multiplication
(4). Rational numbers ka Division
(1). Rational Numbers ka Addition:
Rational number ke addition ke 2 types hote hai:(i) Wo rational numbers, jinka denominator (Har) same ho.
(ii) Wo Rational numbers jinka denominator (Har) different (same nahi) ho.
(i) Wo Rational number jinka denominator (Har) same ho:
Example-1. 2/5 aur 1/5 ke "Har" same hai. Innka addition hum nichey step-by-step karte hai.
Solution: Hume 2/5 aur 1/5 ko add karna hai. Means,
⇒ 2 + 1
5 5
Step-1. Sabse pahle ek line khich kar uske nichey 5 likhe.
Jaise-:
5
Step-2. Ab 5 aur line ke uppar 2+1 likhe.
Jaise-: 2 + 1
5
Step-3. 2+1 = 3 likhkar uske niche 5 likhe. Bas ho gaya.
Jaise-: 2 + 1 = 3 Ans.
5 5
Example-2. Add 5/7 aur 4/7.
Solution-: 5/7 aur 4/7 ke Har = 7 same hai. To inka addition iss prakar se hoga.
5 + 4 = 5+4 = 9 Ans.
7 7 7 7
To ye tha unn rational number ka addition jinka denominator (har) same ho. Ab hum aapko batane jaa rahe hai unn rational number ka addition jinka denominator (har) different ho. To aayie issko bhi sikh lete hai:
(ii) Wo Rational number jinka denominator (Har) different (same nahi) ho:
Example-1. 7/9 aur 5/6 ke Har different (same nahi) hai. Innka addition hum nichey step-by-step karte hai.
Solution: Hume 7/9 aur 5/6 ko add karna hai. Means,
⇒ 7 + 5
9 6
Step-1. Sabse pahle denominator = 9 aur 6 ka L.C.M. nikale.
Jaise-: 2| 6, 9
3| 3, 9
3| 1, 3
| 1, 1
L.C.M. = 2×3×3 = 18
Step-2. Ab ek line khichkar uske niche L.C.M. = 18 likhe.
Jaise-:
18
Step-3. Ab 7/9 ke denominator 9 se L.C.M 18 ko divide karke. Bhagphal me numerator 7 se multiply kare. Issko note kare.
Jaise-: 18÷9 = 2
2×7 = 14
14 +
18
Step-4. Second Rational number 5/6 ke liye bhi same step-3 jaisa hi karenge.
Jaise-: 18÷6 = 3
3×5 = 15
14 + 15 = 29 Ans.
18 18
Example-2. 4/14 aur 3/8 Add kariye.
Solution-: Hume 4/14 aur 3/8 ko add karna hai. Jinke denominator different hai.
⇒ 4 + 3
14 8
Step-1. 14 aur 8 ka L.C.M. nikalenge.
2 | 14, 8
2 | 7, 4
2 | 7, 2
7 | 7, 1
| 1, 1
L.C.M. = 2×2×2×7 = 56
Step-2. 224+21 = 245 Ans.
56 56
(2). Rational Numbers ka Subtraction:
Addition ki tarah se, inn numbers ke subtraction ke bhi 2 types hote hai:(i). Wo Parimey sankhya jinka Har same ho.
(ii). Wo Parimey sankhya jinka Har different ho.
(i) Wo Parimey sankhya jinka Har same ho:
Jis tarah humne addition ke liye jo step ko follow kiya hai. Same wahi steps subtraction me bhi karna hai.
kewal ek change hoga. Addition me hum "plus(+)" ka use karte hai. Jabki subtraction me hum "minus (-)" ka use karenge.
Example: 12/17 me se 8/17 ko subtract kijiye.
Solution-: 12/17 aur 8/17 ke denominator same hai.
12 - 4 = 12 - 4 = 8 Ans.
17 17 17 17
(i) Wo Parimey sankhya jinka Har different (same nahi) ho:
Example: 5/8 aur 9/10 ko subtract kijiye.
Solution: 15/8 aur 9/10 ka denominator (Har) different (same nahi) hai. To isska solution iss prakar se hai:
⇒ 15 - 9
8 10
Step-1. 8 aur 10 ka L.C.M. nikalenge.
2 | 8, 10
2 | 4, 5
2 | 2, 5
5 | 1, 5
| 1, 1
L.C.M. = 2×2×2×5 = 40
Step-2. 75 - 36 = 39 Ans.
40 40
(3). Rational Numbers ka Multiplication:
Kisi bhi two Parimey sankhya ka multiply karna bahot easy hai. Suppose kariye hum two Parimey sankhya -3/5 aur 7/8 ka multiply karna hai. To isske liye hume dono numbers ke numerator -3 aur 7 ka multiply aur denominator 5 aur 8 ka multiply karke divide karna hai.Example-1. -3/5 aur 7/8 ka multiply kijiye.
Solution: -3/5 aur 7/8 ka multiply hum iss prakar se kar sakte hai:
⇒ -3 × 7
5 8
⇒ -3 × 7
5 × 8
⇒ -21 Ans.
40
Agar aapko abhi bhi koi doubt hai to nichey diye steps ko follow kijiye:
Step-1. Dono Parimey sankhya ke numerator ka multiply kare.
Step-2. Dono Parimey sankhya ke denominator ka multiply kare.
Step-3. Denominator ke product ko numerator ke product se divide kare.
Example-2. 13/7 aur -6/15 ka multiply kijiye.
Solution: 13/7 aur 6/15 ka multiply hum iss prakar se kar sakte hai:
⇒ 13 × -6
7 15
⇒ 13 × (-6)
7 × 15
⇒ -78 Ans.
105
(4). Rational Numbers ka Division:
Parimey sankhya ka division, isske multiplication ki tarah hota hai.Kisi number (x) ka kisi other number (y) se divide karne ke liye hume number x ka multiply y ke reciprocal (ulta) 1/y se karna hota hai.
Means, x÷y = x×1/y
Example: 9/13 ko 5/7 se divide kijiye.
Solution: Hume 9/13 ko 5/7 se divide karna hai. Means,
⇒ 9 ÷ 5
13 7
Step-1. Sabse pahle 9/13 ko likhkar "÷" sign ki jagah "×" likhe. aur 5/7 ka reciprocal (ulta) 7/5 karke likhe.
Jaise-: 9 × 7
13 5
Step-2. Ab numerator 9 aur 7 ka aapas me multiply kare aur denominator 13 aur 5 ka aapas me multiply kare.
Jaise-: 9 × 7 = 63 Ans.
13×5 65
Ye bhi padhe-:
❒Natural numbers kya hai ? with example | Properties
❒Equilateral triangle (sambaahu tribhuj) ka area formula proof in hindi
❒Prove that medians of a triangle divides each other in the ratio 2:1
Aaj ke liye itana hi dosto. Hume ummid hai ki, aapko aaj ka topic achhe se samjh aaya hoga.
Agar aapko koi doubt hai ya aap humse koi questions puchhna chahate hai to nichey diye comment box me comment karke puchh sakte hai. Aap chahe to apna question ya question ki image humre Facebook page par massage karke bhi puchh sakte hai.
Hum issi tarah se math ke ek-ek topic ko aapke saath share karte hai. Aap hume bataye ki, Next lesson me aap math ka kon-sa topic sikhna chahte hai? Abhi comment ya massage karke bataye.
Agar aapko aaj ka topic helpful laga ho to please ek share jarur kare.
Multiplicative inverse detail
जवाब देंहटाएंKiska multiplicative inverse jaanaa chahte hai?
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