Hello friend !! Aaj hum aapko whole numbers ke baare me full detail me batayenge. Whole number ke baare me aapke sabhi doubt iss article ko padh karke dur ho jaayenge. Humne iss topic me Whole number ki defination, properties examples ke alawa aur bhi bahot saare whole numbers se related important questions ko issme add kiya hai. Jissase aapko whole numbers ke baare me jaanane me bahot help milegi. To chaliye aaj ka math topic start karte hai. Whole number ko jaanane se pahle hume natural number ke baare me jaanana bahot jaruri hota hai. Humne natural number ke baare me full detail me bataya hai. Aap yaha se padh sakte hai-: Natural numbers kya hai ? with example | Properties
Hum ye ummid karte hai ki, aapne Natural numbers ke baare me padh liya hoga. To ab hum aaj ke topic par aate hai.
Whole numbers ke baare me aap kya-kya sikhenge ?
Aaj aap whole numbers ke baare me jo - jo sikhenge wo iss prakar se nichey diya gaya hai-:
❐ Whole number kya hota hai ?
❐ Whole number ki defination kya hoti hai?
❐ Whole number symbol and examples
❐ Smallest and largest Whole number
❐ first fifty's Whole numbers set.
❐ Kya negative numbers, whole numbers hote hai ?
❐ Whole numbers ki properties.
Smallest whole numbers matlab sabse chhota whole number "0" hai. Sabse largest whole numbers koi nahi hai kyuki har number ka next number (agala number) hota hai.
Hum nichey first fifty's whole numbers ki list de rahe hai-:
Hum ye ummid karte hai ki, aapne Natural numbers ke baare me padh liya hoga. To ab hum aaj ke topic par aate hai.
Whole numbers ke baare me aap kya-kya sikhenge ?
Aaj aap whole numbers ke baare me jo - jo sikhenge wo iss prakar se nichey diya gaya hai-:
❐ Whole number kya hota hai ?
❐ Whole number ki defination kya hoti hai?
❐ Whole number symbol and examples
❐ Smallest and largest Whole number
❐ first fifty's Whole numbers set.
❐ Kya negative numbers, whole numbers hote hai ?
❐ Whole numbers ki properties.
Whole number defination with example and properties in Hindi
Whole number ko hindi me purn sankhya (पूर्ण संख्या ) kahte hai. Purn sankhya ka matalab puri sankhya ( complete number ) hota hai.
Defination of Whole number
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10... ke sabhi numbers ko whole number kahate hai. Matalab whole numbers, decimal numbers (e.g. 1.3, 3.7), fraction numbers (e.g. 1/7, 2/3) aur negative numbers (e.g. -1,-3,-4) nahi hote hai. Agar hum natural number ke set {N = 1, 2, 3, 4...} me 1 ke pahle "0" rakh de {0, 1, 2, 3, 4...} to ye whole number ban jaata hai.
Yaha par ye yaad rakhe ki, "Sabhi natural number, whole number hai lekin sabhi whole number, natural number nahi hai." Kyuki number "0" whole number hai, lekin natural number nahi hai.
Whole numbers ko isski spelling (W H O L E) ke first letter W se denote karte hai. 34, 235, 1345, ... sabhi whole number ke examples hai. first five whole number
W = { 0, 1, 2, 3, 4, 5}
Yaha par ye yaad rakhe ki, "Sabhi natural number, whole number hai lekin sabhi whole number, natural number nahi hai." Kyuki number "0" whole number hai, lekin natural number nahi hai.
❐ Whole number symbol and examples
Whole numbers ko isski spelling (W H O L E) ke first letter W se denote karte hai. 34, 235, 1345, ... sabhi whole number ke examples hai. first five whole number
W = { 0, 1, 2, 3, 4, 5}
❐ Smallest and largest Whole number
Smallest whole numbers matlab sabse chhota whole number "0" hai. Sabse largest whole numbers koi nahi hai kyuki har number ka next number (agala number) hota hai.
❐ first fifty's Whole number
Hum nichey first fifty's whole numbers ki list de rahe hai-:
| 0 | 10 | 20 | 30 | 40 | 50 |
| 1 | 11 | 21 | 31 | 41 | |
| 2 | 12 | 22 | 32 | 42 | |
| 3 | 13 | 23 | 33 | 43 | |
| 4 | 14 | 24 | 34 | 44 | |
| 5 | 15 | 25 | 35 | 45 | |
| 6 | 16 | 26 | 36 | 46 | |
| 7 | 17 | 27 | 37 | 47 | |
| 8 | 18 | 28 | 38 | 48 | |
| 9 | 19 | 29 | 39 | 49 |
❐ Kya negative numbers whole numbers hote hai ?
Nahi, negative numbers (e.g. -1,-2,-3,-4) whole numbers nahi hote hai. Negative numbers wo numbers hote hai jo minus me hote hai. Jaise-: -3, -5, -39, -321 etc.
❐ Whole numbers ki properties
Hum jaante hai ki, math me total 4 operation Addition, subtraction, multiplication aur division hote hai. Whole numbers ke liye inn sabhi operation ke liye kuch properties hoti hai. Wahi properties ko hum niche diye hai.
Properties of addition
1. Closure property -:
Whole numbers ka addition, closure property ko follow karta hai. Kyuki Jab hum koi bhi two whole numbers (suppose 3 aur 6) ko aapas me add (3+6) karte hai to answer (9) hume ek whole numbers milta hai. Iss property ko whole numbers ke addition ka closure property kahte hai.
General formula-: Yadi A aur B whole numbers ho to closure properties ke anusaar -:
A+B = C bhi whole number hoga.
More example-:
• 3+6 = 9 (whole number)
• 7+4 = 11 (whole number)
• 1+5 = 6 (whole number)
• 8+13 = 21 (whole number)
2. Commutative property -:
Whole number ka addition, commutative property ko follow karta hai. Kyuki jab hum koi bhi two whole numbers (suppose 4 aur 5) ko add (4+5 = 9) kare aur phir issi whole numbers (4 aur 5) ke order (kram) ko change karke add (5+4 = 9) kare to dono hi step me hume answer same (equal) hi milta hai. Issi property ko hum whole numbers ke addition ka commutative property kahte hai.
General formula-: Yadi A aur B whole numbers ho to, commutative property ke anusaar-:
A+B = B+A
More example-:
• 3+6 = 9 and 6+3 = 9
So, 3+6 = 6+3
• 7+4 = 11 and 4+7 = 11
So, 7+4 = 4+7
• 1+5 = 6 and 5+1 = 6
So, 1+5 = 5+1
• 8+13 = 21 and 13+8 = 21
So, 8+13 = 13+8
3. Associative property -:
Whole number ka addition, associative property ko follow karta hai. Kyuki Iss property ke anusaar agar hum koi bhi three whole numbers (suppose 2,4 aur 7) ko two whole number ka group banakar add kare. Jaise-: (2+4)+7 = 6+7 = 13
Phir iss group ko change karke add kare. Jaise-: 2+(4+7) = 2+11 = 13 to dono ka answer same (equal) hota hai. Issi property ko whole numbers ke addition ka associative property kahte hai.
General formula-: Yadi A, B aur C koi three whole numbers ho to, associative property ke anusaar-:
(A+B)+C = A+(B+C)
More example-:
• (2+3)+4 = 5+4 = 9 and 2+(3+4) = 2+7 = 9
So, (2+3)+4 = 2+(3+4)
• (5+6)+7 = 11+7 = 18 and 5+(6+7) = 5+13 = 18
So, (5+6)+7 = 5+(6+7)
• (8+9)+10 = 17+10 = 27 and 8+(9+10) = 27
So, (8+9)+10 = 8+(9+10)
4. Additive identity -:
Zero "0" ko whole number ka additive identity kahte hai. Iss additive identity ke anusaar , agar hum kisi bhi whole number (suppose 4) ko Iss additive identity (0) me add (0+4 = 4 = 4+0) kare to hume wahi whole number (4) hi milta hai.
General formula-: Yadi koi whole number A ho to additive identity ke anusaar-: A+0 = A = 0+A
More example-:
• 0+2 = 2 or 2+0 = 2
• 0+5 = 5 or 5+0 = 5
• 0+13 = 13 or 13+0 = 13
Properties of subtraction
1. Closure property -:
Whole number ka Subtraction, closure property ko follow nahi karta hai. Kyuki jab hum koi two whole numbers (suppose 3 aur 6) ko subtract (3-6) karte hai to ye jaruri nahi hai ki answer (3-6 = -3) hume ek whole numbers mile.
General formula-: Yadi A aur B two whole numbers ho to closure property ke anusaar-:
A-B = C , Jaruri nahi ki "C" humesha whole number ho.
More example-:
• 5-2 = 3 (whole number) but 2-5 = -3 (whole number nahi)
• 7-6 = 1 (whole number) but 6-7 = -1 (whole number nahi)
• 8-4 = 4 (whole number) but 4-8 = -4 (whole number nahi)
2. Commutative property -:
Whole number ka subtraction, commutative property ko follow nahi karta hai. Kyuki jab hum koi two whole numbers (suppose 9 aur 5) ko subtract (9-5 = 4) kare aur phir issi whole numbers (9 aur 5) ke order (kram) ko change karke subtract (5-9 = -4) kare to hume answer same (equal) nahi milta hai.
General formula-: Yadi A aur B whole numbers ho to , commutative property ke anusaar-:
A-B ≠B-A
More example-:
• 5-3 = 2 and 3-5 = -2
So, 5-3 ≠ 3-5
• 7-2 = 5 and 2-7 = -5
So, 7-2 ≠ 2-7
• 12-8 = 4 and 8-12 = -4
So, 12-8 ≠ 8-12
3. Associative property -:
Whole number ka subtraction, associative property ko bhi follow nahi karta kyuki, Jab hum koi bhi three whole numbers (suppose 9,3 aur 4) ko two whole number ka group banakar subtract kare. Jaise-: (9-3)-4 = 6-4 = 2
Phir iss group ko change karke subtract kare. Jaise-: 9-(3-4) = 9-(-1) = 9+1 = 10 to do step ka answer equal nahi hota hai.
General formula-: Yadi A, B aur C whole numbers ho to associative property ke anusaar-:
(A-B)-C ≠ A-(B-C)
More example-:
• (7-1)-3 = 6-3 = 3 and 7-(1-3) = 7-(-2) = 7+2 = 9
So, (7-1)-3 ≠ 7-(1-3)
• (8-2)-4 = 6-4 = 2 and 8-(2-4) = 8-(-2) = 8+2 = 10
So, (8-2)-4 ≠ 8-(2-4)
• (9-3)-5 = 6-5 = 1 and 9-(3-5) = 9-(-2) = 9+2 = 11
So, (9-3)-5 ≠ 9-(3-5)
4. Subtract zero property-:
Subtract zero property ke anusaar, Jab hum kisi bhi whole number me se Zero "0" subtract karte hai to hume wahi whole number hi milta hai.
Jaise-: 5-0 = 5, 12-0 = 12
General formula-: Yadi A koi whole number ho to iss property ke anusaar-: A-0 = A
More example-:
• 2-0 = 2
• 8-0 = 8
• 14-0 = 14
Properties of multiplication
1. Closure property -:
Whole number ka multiplication closure property ko follow karta hai. Kyuki jab hum koi bhi two whole numbers (Suppose 3 aur 6) ko aapas me multiply (3×6) karte hai to answer (3×6 = 18) hume ek whole numbers milta hai.
General formula-: Yadi A aur B whole numbers ho to closure property ke anusaar-:
A×B = C whole number hoga.
More example-:
• 4×5 = 20 (whole number)
• 6×3 = 18 (whole number)
• 9×8 = 72 (whole number)
2. Commutative property -:
Whole number ka multiplication ccommutative property ko follow karta hai. Kyuki jab hum koi bhi two whole numbers (suppose 4 aur 5) ka multiply (4×5 = 20) kare aur phir issi whole numbers (4 aur 5) ke order (kram) ko change karke multiply (5×4 = 20) kare to hume answer same milta hai.
General formula-: Yadi A aur B whole numbers ho to, commutative property ke anusaar-:
A×B = B×A
More example-:
• 2×3 = 6 and 3×2 = 6
So, 2×3 = 3×2
• 4×5 = 20 and 5×4 = 20
So, 4×5 = 5×4
• 7×8 = 56 and 8×7 = 56
So, 7×8 = 8×7
3. Associative property -:
Whole number ka multiplication associative property ko follow karta hai. Kyuki Iss property ke anusaar agar hum koi bhi three whole numbers (suppose 2,4 aur 7) ko two whole number ka group banakar multiply kare. Jaise-: (2×4)×7 = 8×7 = 56
Phir iss group ko change karke add kare. Jaise-: 2×(4×7) = 2×28 = 56 to dono ka answer equal hota hai. Issi property ko associative property kahte hai.
General formula-: Yadi A, B aur C koi three whole numbers ho to, associative property ke anusaar-:
(A×B)×C = A×(B×C)
More example-:
• (1×2)×3 = 2×3 = 6 and 1×(2×3) = 1×6 = 6
So, (1×2)×3 = 1×(2×3)
• (4×5)×7 = 20×7 = 140 and 4×(5×7) = 4×35 = 140
So, (4×5)×7 =4×(5×7)
• (8×9)×10 = 72×10 = 720 and 8×(9×10) = 8×90 = 720
So, (8×9)×10 = 8×(9×10)
4. Multiplicative identity -:
One "1" ko whole number ka multiplicative identity kahte hai. Iss identity ke anusaar , agar hum kisi bhi whole number (4) ko Iss identity (1) se multiply kare (1×4 = 4 = 4×1) kare to hume wahi whole number (4) hi milta hai.
General formula-: Yadi koi whole number A ho to multiplicative identity ke anusaar-: A×1 = A = 1×A
More example-:
• 4×1 = 4 = 1×4
• 5×1 = 5 = 1×5
• 6×1 = 6 = 1×6
5. Multiplication zero property-:
Multiplication zero property ke anusaar, Jab hum kisi bhi whole number ko Zero "0" se multiply karte hai to hume humesha "0" hi milta hai.
Jaise-: 5×0 = 0, 12×0 = 0
General formula-: Yadi A koi whole number ho to iss property ke anusaar-: A×0 = 0 = 0×A
More example-:
• 7×0 = 0 = 7×0
• 8×0 = 0 = 8×0
• 9×0 = 0 = 9×0
Properties of Division
1. Closure property -:
Whole number ka Division closure property ko follow nahi karta hai. Kyuki jab hum koi two whole numbers (suppose 3 aur 6) ko divide (3÷6) karte hai to ye jaruri nahi hai ki answer (3÷6 = 3/6 = 1/2) hume ek whole numbers mile.
General formula-: Yadi A aur B two whole numbers ho to closure property ke anusaar-:
A÷B = C , Jaruri nahi ki "C" humesha whole number ho.
More example-:
• 4÷2 = 2 (whole number)
• 5÷2 = 5/2 (whole number nahi hai)
• 12÷3 = 4 (whole number)
• 14÷8 = 14/8 = 7/4 (whole number nahi hai)
2. Commutative property -:
Whole number ka Division commutative property ko follow nahi karta hai. Kyuki jab hum koi two whole numbers (suppose 9 aur 3) ko divide (9÷3 = 3) kare aur phir issi whole numbers (9 aur 3) ke order (kram) ko change karke divide (3÷9 = 1/3) kare to hume answer same (equal) nahi milta hai.
General formula-: Yadi A aur B koi two whole numbers ho to, commutative property ke anusaar-:
A÷B ≠B÷A
More example-:
• 6÷2 = 3 and 2÷6 = 2/6 = 1/3
So, 6÷2 ≠ 2÷6
• 8÷4 = 2 and 4÷8 = 4/8 = 1/2
So, 8÷4 ≠ 4÷8
• 12÷3 = 4 and 3÷12 = 3/12 = 1/4
So, 12÷3 ≠ 3÷12
3. Associative property -:
Whole number ka Division, associative property ko bhi follow nahi karta kyuki, Jab hum koi bhi three whole numbers (suppose 12,3 aur 2) ko two whole number ka group banakar divide kare. Jaise-: (12÷3)÷2 = 4÷2 = 2
Phir iss group ko change karke divide kare. Jaise-: 12÷(3÷2) = 12÷3/2 = 12×2/3 = 8 to dono step me answer equal nahi hota hai.
General formula-: Yadi A, B aur C whole numbers ho to associatI've property ke anusaar-:
(A÷B)÷C ≠ A÷(B÷C)
More example-:
• (15÷3)÷5 = 5÷5 = 1 and 15÷(3÷5) = 15÷3/5 = 15×5/3 = 5×5 = 25
So, (15÷3)÷5 ≠ 15÷(3÷5)
• (12÷2)÷3 = 6÷3 = 2 and 12÷(2÷3) = 12÷2/3 = 12×3/2 = 6×3 = 18
So, (12÷2)÷3 ≠ 12÷(2÷3)
• (24÷3)÷4 = 8÷4 = 2 and 24÷(3÷4) = 24÷3/4 = 24×4/3 = 8×4 = 32
So, (24÷3)÷4 ≠ 24÷(3÷4)
4. Division by 1-:
Jab hum kisi bhi whole number (5) ko "1" se divide (5÷1) karte hai to hume wahi whole number (5) hi milta hai.
General formula-:Yadi A koi whole number ho to 1 se A ko divide karne par-: A÷1 = A
Whole number ka Division closure property ko follow nahi karta hai. Kyuki jab hum koi two whole numbers (suppose 3 aur 6) ko divide (3÷6) karte hai to ye jaruri nahi hai ki answer (3÷6 = 3/6 = 1/2) hume ek whole numbers mile.
General formula-: Yadi A aur B two whole numbers ho to closure property ke anusaar-:
A÷B = C , Jaruri nahi ki "C" humesha whole number ho.
More example-:
• 4÷2 = 2 (whole number)
• 5÷2 = 5/2 (whole number nahi hai)
• 12÷3 = 4 (whole number)
• 14÷8 = 14/8 = 7/4 (whole number nahi hai)
2. Commutative property -:
Whole number ka Division commutative property ko follow nahi karta hai. Kyuki jab hum koi two whole numbers (suppose 9 aur 3) ko divide (9÷3 = 3) kare aur phir issi whole numbers (9 aur 3) ke order (kram) ko change karke divide (3÷9 = 1/3) kare to hume answer same (equal) nahi milta hai.
General formula-: Yadi A aur B koi two whole numbers ho to, commutative property ke anusaar-:
A÷B ≠B÷A
More example-:
• 6÷2 = 3 and 2÷6 = 2/6 = 1/3
So, 6÷2 ≠ 2÷6
• 8÷4 = 2 and 4÷8 = 4/8 = 1/2
So, 8÷4 ≠ 4÷8
• 12÷3 = 4 and 3÷12 = 3/12 = 1/4
So, 12÷3 ≠ 3÷12
3. Associative property -:
Whole number ka Division, associative property ko bhi follow nahi karta kyuki, Jab hum koi bhi three whole numbers (suppose 12,3 aur 2) ko two whole number ka group banakar divide kare. Jaise-: (12÷3)÷2 = 4÷2 = 2
Phir iss group ko change karke divide kare. Jaise-: 12÷(3÷2) = 12÷3/2 = 12×2/3 = 8 to dono step me answer equal nahi hota hai.
General formula-: Yadi A, B aur C whole numbers ho to associatI've property ke anusaar-:
(A÷B)÷C ≠ A÷(B÷C)
More example-:
• (15÷3)÷5 = 5÷5 = 1 and 15÷(3÷5) = 15÷3/5 = 15×5/3 = 5×5 = 25
So, (15÷3)÷5 ≠ 15÷(3÷5)
• (12÷2)÷3 = 6÷3 = 2 and 12÷(2÷3) = 12÷2/3 = 12×3/2 = 6×3 = 18
So, (12÷2)÷3 ≠ 12÷(2÷3)
• (24÷3)÷4 = 8÷4 = 2 and 24÷(3÷4) = 24÷3/4 = 24×4/3 = 8×4 = 32
So, (24÷3)÷4 ≠ 24÷(3÷4)
4. Division by 1-:
Jab hum kisi bhi whole number (5) ko "1" se divide (5÷1) karte hai to hume wahi whole number (5) hi milta hai.
General formula-:Yadi A koi whole number ho to 1 se A ko divide karne par-: A÷1 = A
More example-:
• 2÷1 = 2
• 4÷1 = 4
• 7÷1 = 7
Distributive property of multiplication over addition
Whole number iss property ko follow karta hai. Iss property ke anusaar whole number ka multiplication , whole number ke addition par distrbute hota hai.
General formula-: Yadi A, B aur C three whole number ho to iss property ke anusaar-:
A×(B+C) = (A×B)+(A×C)
Example-: Yadi 2,4 aur 6 three whole number ho to iss property ke anusaar-:
• 2×(4+6) = 2×10 = 20 and (2×4)+(2×6) = 8+12 = 20
So, 2×(4+6) = (2×4)+(2×6)
• 5×(6+7) = 5×13 = 65 and (5×6)+(5×7) = 30+35 = 65
So, 5×(6+7) = (5×6)+(5×7)
• 9×(8+12) = 9×20 = 180 and (9×8)+(9×12) = 72+108 = 180
So, 9×(8+12) = (9×8)+(9×12)
Distributive property of multiplication over subtraction
General formula-: Yadi A, B aur C three whole number ho to iss property ke anusaar-:
A×(B-C) = (A-B)+(A-C)
Example-: Yadi 5, 9 and 8 three whole number ho to iss property ke anusaar-:
• 5×(9-8) = 5×1 = 5 and (5×9)-(5×8) = 45-40 = 5
So, 5×(9-8) = (5×9)-(5×8)
• 7×(8-6) = 7×2 = 14 and (7×8)-(7×6) = 56-42 = 14
So, 7×(8-6) = (7×8)-(7×6)
• 13×(16-8) = 13×8 = 104 and (13×16)-(13×8) = 208-104 = 104
So, 13×(16-8) = (13×16)-(13×8)
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I hope ki, ab aap whole number ke baare me achhe se jaan gaye honge. Agar phir bhi aapko koi doubt (problem) ho to comment karke puchh sakte hai. Hum aapki puri help karne ki koshish karenge.
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