Natural numbers kya hai ? with example | Properties

• Natural numbers kya hai ?
• Natural numbers ka defination kya hai ?
• Iss number ke example kon-kon se numbers hai ?
• Kya "0" natural number hai ?
• Properties of natural number kya hai ?

Agar aap inn sabhi questions ke answer jaanana chahte hai to aap bilkul right place par aaye ho.
Hello friend !! Sabse pahle to agar aap first time humare iss blog par aaye hai to Maths Tricks in Hindi  par hum aapka swagat (welcome) karte hai. Iss blog par hum math ke tricks , mathematics ke topics, math ke questions etc. hindi me aapke saath share karte hai.

Agar aapko math ke kisi topics ya kisi math question me problem ho rahi hai to aap humare  facebook page par massage ya nichey diye comment box ki help se comment karke puchh sakte hai. Hum aapki help karne ki puri koshish karenge. Chaliye hum aapne aaj ke topic par aate hai. Sabse pahle baat karte hai ki, Natural numbers kya hota hai ?

• What is the natural number ?

Natural number ko hindi me prakritik sankhya (प्राकृतिक संख्या ) kahate hai. Kya aapko yaad hai ki jab aap nursery ( K.G) class me the tab aapne math subject me sabse pahle kya sikha tha ?
I'm sure ki aap kahenge ki , 1,2,3,4,5...
Bas yahi number hi to natural numbers hai.
Natural number se hi hum math padana start karte hai. Hum sabhi ko kisi bhi chijo (objects) ko count karna (ginana) ho to hum aise count karna start karte hai:

1,2,3,4,5.... bas yahi counting number ko hi hum natural numbers kahate hai.

• Defination of natural number-:

Sabhi   counting number  ( jinko hum count karne me use karte hai ) ko hum Natural number kahate hai.
Natural number ko isske spelling ke first letter N se denote karte hai. Matlab ki natural numbers ke set ko hum iss prakar se present karte hai-:
N = { 1,2,3,4,5...}
Natural number ko hum number line ya sankhya rekha par iss prakar se present karte hai-:

• Kya natural number, negative number ho sakta hai ?

Nahi , natural numbers kabhi bhi negative numbers nahi ho sakte . Kyuki hum pahle hi bata chuke hai ki , kewal counting number ko hi hum natural number kahate hai. To kya aapne kabhi kisi chijo ko count karne ke liye negative numbers -1,-2,-3,... ka use kiya hai ? Jaise aapne garden ke trees ko aise count kiya-: -1 tree, -2 tree, -3 tree ... I'm sure ki aapka answer "No" hoga. Isliye natural number , negative number nahi ho sakte hai.
• Is "0" a natural number ? (Kya 0 natural number hai ?)

Humare mind me ye question jarur aata hai ki, kya 0 natural number hai? To iska answer hai - "Nahi" , zero natural number nahi hai kyuki hum sabhi kisi bhi objects ko 1 se count karna start karte hai, zero se nahi.

• Natural number ki properties:

Natural number ki kuch properties hoti hai jo niche point to point hum bata rahe hai.

1.  Closure property  

(i) Addition-: Agar hum koi bhi  2 natural numbers ( a and b ) ko  add  kare ( a+b ) to hume humesha hume ek natural number milta hai. Iss property ko hum " closure property of addition " kahte hai. Iss prakar se hum kah sakte hai ki N , addition se closed hai.

Example: Hum jaante hai ki, 4 and 5 natural number hai to inka sum 4+5=9 bhi ek natural number hai.

(ii) Subtraction-: Yadi hum kisi  2 natural numbers ( a aur b ) ko subtract kare ( a-b ) to ye jaruri nahi hai ki hume humesha natural number hi mlile. Iss prakar se hum kah sakte hai ki N , subtraction se closed nahi hai.

Example: 4 - 5 = -1 natural nahi hai.

(iii) Multiplication-: Kisi bhi 2 natural numbers a aur b ka multiply kare (a × b) to hume humesha hume ek natural number milta hai. Iss prakar se hum kah sakte hai ki N , multiplication se closed hai.

Example: 4×5 = 20 natural number hai.

(iv) Division-: Kisi bhi 2 natural numbers a aur b ka divide kare (a ÷ b) to ye jaruri nahi hai ki hume humesha natural number hi mlile. Iss prakar se hum kah sakte hai ki N , division se closed nahi hai.

Example: 4÷5 = 4/5 natural number nahi hai.

2.  Commutative property  

(i) Addition-: Kisi bhi 2 natural numbers (a aur b) ka addition humesha commutative hota hai.
Means, a+b = b+a

Example: 4+5 = 9 aur 5+4 = 9 to iss prakar se 4+5 = 5+4

(ii) Subtraction-: Koi bhi 2 natural numbers ka subtraction commutative nahi hota hai.
Means, a-b ≠ b-a

Example: 8-2 = 6 aur 2-8 = -6 to hum kah sakte hai ki 8-2 ≠ 2-8

(iii) Multiplication-: 2 natural numbers ka multiplication humesha commutative hota hai.
Means, a×b = b×a

Example: 4×5 = 20 aur 5×4 = 20 to hum kah sakte hai ki 4×5 = 5×4

(iv) Division-: kisi bhi 2 natural number ka division commutative nahi hota hai.
Means, a÷b ≠ b÷a

Example: 8÷2 = 4 and 2÷8 = 1/4 to hum kah sakte hai ki, 8÷2 ≠ 2÷8



3.  Associative property  

(i) Addition-: Natural number ka addition associative hota hai.
Means, agar hum koi 3 natural numbers a , b aur c ko choose kare to wo nichye diye rule ko follow karega : a+(b+c) = (a+b)+c 

Example: 4+(5+2) = 4+(7) = 11 aur (4+5)+2 = (9)+2 = 11 to hum kah sakte hai ki 4+(5+2) = (4+5)+2

(ii) Subtraction-: Natural number ka subtraction associative nahi hota hai.
Means,  a-(b-c) ≠ (a-b)-c 

Example: 8-(6-2) = 8-(4) = 4 aur (8-6)-2 = (2)-2 = 0 to hum dekh sakte hai ki, 8-(6-2) ≠ (8-6)-2

(iii) Multiplication-: Natural number ka multiplication associative hota hai.
Means,  a×(b×c) = (a×b)×c 

Example: 2×(3×4) = 2×(12) = 24 aur (2×3)×4 = (6)×4 = 24 to hum dekh sakte hai ki, 2×(3×4) = (2×3)×4

(iv) Division-: Natural number ka division associative nahi hota hai.

Means,  a÷(b÷c) ≠ (a÷b)÷c 

Example: 6÷(8÷4) = 6÷(2) = 3 aur (6÷8)÷4 = (6/8)÷4 = 3/16 = 0.1875 To hum kah sakte hai ki, 6÷(8÷4) ≠ (6÷8)÷4

4. Multiplicative identity  

Kisi natural number a ka multiply 1 se karne par hume multiplication results a milta hai to "1" ko hum  multiplicative identity  kahate hai.
Means, a×1 = 1×a = a

Example: 4×1 = 1×4 = 4

5.  Distributive property 

Distributive property 2 types ke hote hai:
(i) Distributive property of multiplication over addition
(ii) Distributive property of multiplication over subtraction
(i) Distributive property of multiplication over addition

Yadi a, b, aur c koi 3 natural number ho to ye 3 numbers iss property ko follow karte hai.
Means, a×(b+c) = ab+ac

Example: 3×(4+5) = 3×(9) = 27 aur 3×4+3×5 = 12+15 = 27



(ii) Distributive property of multiplication over subtraction

Yadi a, b, aur c koi 3 natural number ho to ye 3 numbers iss property ko follow karte hai.
Means, a×(b-c) = ab-ac

Example: 3×(6-2) = 3×(4) = 12 aur 3×6-3×2 = 18-6 = 12

To friend, natural number ke sabhi properties ko humne dekha aur samjha. Aaj ka topic natural number kya hai ? Example | properties me bas itana hi. I hope ki aapko aaj ka topic achhe se samjh aaya hoga.
Agar phir bhi koi doubt , problem , kisi point me doubt, ya kisi bhi line me dikkat ho rahi hai to abhi nichey diye comment box me comment karke puchhiye. Hum puri kosish karenge ki, aapki problem ya doubt dur kar sake.
Agar aapko humara aaj ka topic accha laga to please only one share karke humari help kariye.
Thanks for reading !!

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