பெருக்கல் அட்டவணையை விரைவாகவும் எளிதாகவும் கற்றுக்கொள்வது எப்படி

பெருக்கல் ஒரே மாதிரியான சொற்களின் கூட்டுத்தொகையாகக் குறிப்பிடப்படும் ஒரு கணிதச் செயல்பாடாகும்.

பெருக்கத்தின் பொதுவான கொள்கை

உதாரணமாக, a ⋅ b (“a times b” என்று படிக்கவும்) என்பது நாம் விதிமுறைகளை தொகுக்கிறோம் என்று அர்த்தம் a, இதன் எண்ணிக்கை சமம் b. ஒரு பெருக்கத்தின் முடிவு ஒரு தயாரிப்பு என்று அழைக்கப்படுகிறது.

எடுத்துக்காட்டுகள்:

• 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

  (ஆறு முறை இரண்டு)

• 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20

  (நான்கு முறை ஐந்து)

• 3 ⋅ 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24

  (எட்டு முறை மூன்று)

நாம் அறிந்தபடி, காரணிகளின் இடங்களின் வரிசைமாற்றத்திலிருந்து, தயாரிப்பு மாறாது. மேலே உள்ள எடுத்துக்காட்டுகளுக்கு, இது மாறிவிடும்:

• 6 ⋅ 2 = 6 + 6 = 12

  (இரண்டு முறை ஆறு)

• 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20

  (ஐந்து முறை நான்கு)

• 8 ⋅ 3 = 8 + 8 + 8 = 24

  (மூன்று முறை எட்டு)

நடைமுறை நன்மைகள்

பெருக்கலுக்கு நன்றி, ஒரே மாதிரியான பொருட்களின் மொத்த எண்ணிக்கையை நீங்கள் கணிசமாகக் குறைக்கலாம். எடுத்துக்காட்டாக, எங்களிடம் 7 தொகுப்புகள் இருந்தால், ஒவ்வொன்றிலும் 5 பேனாக்கள் இருந்தால், இவற்றைப் பெருக்குவதன் மூலம் மொத்த பேனாக்களின் எண்ணிக்கை கண்டறியப்படும். இரண்டு எண்கள்:

5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35

(ஐந்து பேனாக்கள் ஏழு முறை)

0 ஆல் பெருக்கவும்

முடிவு எப்போதும் பூஜ்ஜியமாகும்.

• 0 ⋅ 0 = 0
• 1 ⋅ 0 = 0 ⋅ 1 = 0
• 2 ⋅ 0 = 0 ⋅ 2 = 0 + 0 = 0
• 3 ⋅ 0 = 0 ⋅ 3 = 0 + 0 + 0 = 0
• 4 ⋅ 0 = 0 ⋅ 4 = 0 + 0 + 0 + 0 = 0
• 5 ⋅ 0 = 0 ⋅ 5 = 0 + 0 + 0 + 0 + 0 = 0
• 6 ⋅ 0 = 0 ⋅ 6 = 0 + 0 + 0 + 0 + 0 + 0 = 0
• 7 ⋅ 0 = 0 ⋅ 7 = 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
• 8 ⋅ 0 = 0 ⋅ 8 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
• 9 ⋅ 0 = 0 ⋅ 9 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
• 10 ⋅ 0 = 0 ⋅ 10 = 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0

1 ஆல் பெருக்கவும்

தயாரிப்பு ஒன்றைத் தவிர மற்றொரு பெருக்கிக்கு சமம்.

• 1 ⋅ 1 = 1
• 2 ⋅ 1 = 2 ⋅ 1 = 2
• 3 ⋅ 1 = 3 ⋅ 1 = 3
• 4 ⋅ 1 = 4 ⋅ 1 = 4
• 5 ⋅ 1 = 5 ⋅ 1 = 5
• 6 ⋅ 1 = 6 ⋅ 1 = 6
• 7 ⋅ 1 = 7 ⋅ 1 = 7
• 8 ⋅ 1 = 8 ⋅ 1 = 8
• 9 ⋅ 1 = 9 ⋅ 1 = 9
• 10 ⋅ 1 = 10 ⋅ 1 = 10

2 ஆல் பெருக்கவும்

முதல் காரணியை அதனுடன் சேர்க்கவும்.

• 1 ⋅ 2 = 1 + 1 = 2
• 2 ⋅ 2 = 2 + 2 = 4
• 3 ⋅ 2 = 3 + 3 = 6
• 4 ⋅ 2 = 4 + 4 = 8
• 5 ⋅ 2 = 5 + 5 = 10
• 6 ⋅ 2 = 6 + 6 = 12
• 7 ⋅ 2 = 7 + 7 = 14
• 8 ⋅ 2 = 8 + 8 = 16
• 9 ⋅ 2 = 9 + 9 = 18
• 10 ⋅ 2 = 10 + 10 = 20

3 ஆல் பெருக்கவும்

முதல் காரணியை 2 ஆல் பெருக்குகிறோம், பின்னர் அதை முடிவில் சேர்க்கிறோம்.

• 1 ⋅ 3 = (1 ⋅ 2) + 1 = 2 + 1 = 3
• 2 ⋅ 3 = (2 ⋅ 2) + 2 = 4 + 2 = 6
• 3 ⋅ 3 = (3 ⋅ 2) + 3 = 6 + 3 = 9
• 4 ⋅ 3 = (4 ⋅ 2) + 4 = 8 + 4 = 12
• 5 ⋅ 3 = (5 ⋅ 2) + 5 = 10 + 5 = 15
• 6 ⋅ 3 = (6 ⋅ 2) + 6 = 12 + 6 = 18
• 7 ⋅ 3 = (7 ⋅ 2) + 7 = 14 + 7 = 21
• 8 ⋅ 3 = (8 ⋅ 2) + 8 = 16 + 8 = 24
• 9 ⋅ 3 = (9 ⋅ 2) + 9 = 18 + 9 = 27
• 10 ⋅ 3 = (10 ⋅ 2) + 10 = 20 + 10 = 30

4 ஆல் பெருக்கவும்

இரட்டிப்பாக்கப்பட்ட முதல் காரணிக்கு அதே தொகையைச் சேர்க்கிறோம்.

• 1 ⋅ 4 = (1 ⋅ 2) + (1 ⋅ 2) = 2 + 2 = 4
• 2 ⋅ 4 = (2 ⋅ 2) + (2 ⋅ 2) = 4 + 4 = 8
• 3 ⋅ 4 = (3 ⋅ 2) + (3 ⋅ 2) = 6 + 6 = 12
• 4 ⋅ 4 = (4 ⋅ 2) + (4 ⋅ 2) = 8 + 8 = 16
• 5 ⋅ 4 = (5 ⋅ 2) + (5 ⋅ 2) = 10 + 10 = 20
• 6 ⋅ 4 = (6 ⋅ 2) + (6 ⋅ 2) = 12 + 12 = 24
• 7 ⋅ 4 = (7 ⋅ 2) + (7 ⋅ 2) = 14 + 14 = 28
• 8 ⋅ 4 = (8 ⋅ 2) + (8 ⋅ 2) = 16 + 16 = 32
• 9 ⋅ 4 = (9 ⋅ 2) + (9 ⋅ 2) = 18 + 18 = 36
• 10 ⋅ 4 = (10 ⋅ 2) + (10 ⋅ 2) = 20 + 20 = 40

5 ஆல் பெருக்கவும்

மற்ற பெருக்கி இரட்டை எண்ணாக இருந்தால், முடிவு பூஜ்ஜியத்திலும், ஒற்றைப்படை என்றால், எண் 5ல் முடிவடையும்.

• 1 ⋅ 5 = 5 ⋅ 1 = 5
• 2 ⋅ 5 = 5 ⋅ 2 = 5 + 5 = 10
• 3 ⋅ 5 = 5 ⋅ 3 = (5 ⋅ 2) + 5 = 15
• 4 ⋅ 5 = 5 ⋅ 4 = (5 ⋅ 2) + (5 ⋅ 2) = 20
• 5 ⋅ 5 = 5 + 5 + 5 + 5 + 5 = 25
• 6 ⋅ 5 = 5 ⋅ 6 = (5 ⋅ 5) + 5 = 30
• 7 ⋅ 5 = 5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
• 8 ⋅ 5 = 5 ⋅ 8 = (5 ⋅ 4) + (5 ⋅ 4) = 40
• 9 ⋅ 5 = 5 ⋅ 9 = (5 ⋅ 10) - 5 = 45
• 10 ⋅ 5 = 5 ⋅ 10 = 50

6 ஆல் பெருக்கவும்

முதல் காரணியை 5 ஆல் பெருக்கி, அதன் முடிவை அதில் சேர்க்கவும்.

• 1 ⋅ 6 = (1 ⋅ 5) + 1 = 5 + 1 = 6
• 2 ⋅ 6 = (2 ⋅ 5) + 2 = 10 + 2 = 12
• 3 ⋅ 6 = (3 ⋅ 5) + 3 = 15 + 3 = 18
• 4 ⋅ 6 = (4 ⋅ 5) + 4 = 20 + 4 = 24
• 5 ⋅ 6 = (5 ⋅ 5) + 5 = 25 + 5 = 30
• 6 ⋅ 6 = (6 ⋅ 5) + 6 = 30 + 6 = 36
• 7 ⋅ 6 = (7 ⋅ 5) + 7 = 35 + 7 = 42
• 8 ⋅ 6 = (8 ⋅ 5) + 8 = 40 + 8 = 48
• 9 ⋅ 6 = (9 ⋅ 5) + 9 = 45 + 9 = 54
• 10 ⋅ 6 = (10 ⋅ 5) + 10 = 50 + 10 = 60

7 ஆல் பெருக்கவும்

7 ஆல் பெருக்குவதற்கு எளிமையான வழிமுறை எதுவும் இல்லை, எனவே மற்ற காரணிகளுக்குப் பொருந்தும் முறைகளைப் பயன்படுத்துகிறோம்.

• 1 ⋅ 7 = 7 ⋅ 1 = 7
• 2 ⋅ 7 = 7 ⋅ 2 = 7 + 7 = 14
• 3 ⋅ 7 = 7 ⋅ 3 = (7 ⋅ 2) + 7 = 21
• 4 ⋅ 7 = 7 ⋅ 4 = (7 ⋅ 2) + (7 ⋅ 2) = 28
• 5 ⋅ 7 = 7 ⋅ 5 = 7 + 7 + 7 + 7 + 7 = 35
• 6 ⋅ 7 = 7 ⋅ 6 = (7 ⋅ 5) + 7 = 42
• 7 ⋅ 7 = 7 + 7 + 7 + 7 + 7 + 7 + 7 = 49
• 8 ⋅ 7 = 7 ⋅ 8 = (7 ⋅ 4) + (7 ⋅ 4) = 56
• 9 ⋅ 7 = 7 ⋅ 9 = (7 ⋅ 10) - 7 = 63
• 10 ⋅ 7 = 70

8 ஆல் பெருக்கவும்

நாம் முதல் காரணியை 4 ஆல் பெருக்குகிறோம், பின்னர் அதே தொகையை முடிவில் சேர்க்கவும்.

• 1 ⋅ 8 = (1 ⋅ 4) + (1 ⋅ 4) = 8
• 2 ⋅ 8 = (2 ⋅ 4) + (2 ⋅ 4) = 16
• 3 ⋅ 8 = (3 ⋅ 4) + (3 ⋅ 4) = 24
• 4 ⋅ 8 = (4 ⋅ 4) + (4 ⋅ 4) = 32
• 5 ⋅ 8 = (5 ⋅ 4) + (5 ⋅ 4) = 40
• 6 ⋅ 8 = (6 ⋅ 4) + (6 ⋅ 4) = 48
• 7 ⋅ 8 = (7 ⋅ 4) + (7 ⋅ 4) = 56
• 8 ⋅ 8 = (8 ⋅ 4) + (8 ⋅ 4) = 64
• 9 ⋅ 8 = (9 ⋅ 4) + (9 ⋅ 4) = 72
• 10 ⋅ 8 = (10 ⋅ 4) + (10 ⋅ 4) = 80

9 ஆல் பெருக்கவும்

முதல் காரணியை 10 ஆல் பெருக்குகிறோம், பின்னர் பெறப்பட்ட முடிவிலிருந்து அதைக் கழிப்போம்.

• 1 ⋅ 9 = (1 ⋅ 10) – 1 = 10 – 1 = 9
• 2 ⋅ 9 = (2 ⋅ 10) – 2 = 20 – 2 = 18
• 3 ⋅ 9 = (3 ⋅ 10) – 3 = 30 – 3 = 27
• 4 ⋅ 9 = (4 ⋅ 10) – 4 = 40 – 4 = 36
• 5 ⋅ 9 = (5 ⋅ 10) – 5 = 50 – 5 = 45
• 6 ⋅ 9 = (6 ⋅ 10) – 6 = 60 – 6 = 54
• 7 ⋅ 9 = (7 ⋅ 10) – 7 = 70 – 7 = 63
• 8 ⋅ 9 = (8 ⋅ 10) – 8 = 80 – 8 = 72
• 9 ⋅ 9 = (9 ⋅ 10) – 9 = 90 – 9 = 81
• 10 ⋅ 9 = (10 ⋅ 10) – 10 = 100 – 10 = 90

10 ஆல் பெருக்கவும்

மற்ற பெருக்கியின் முடிவில் பூஜ்ஜியத்தைச் சேர்க்கவும்.

• 1 ⋅ 10 = 10 ⋅ 1 = 10
• 2 ⋅ 10 = 10 ⋅ 2 = 20
• 3 ⋅ 10 = 10 ⋅ 3 = 30
• 4 ⋅ 10 = 10 ⋅ 4 = 40
• 5 ⋅ 10 = 10 ⋅ 5 = 50
• 6 ⋅ 10 = 10 ⋅ 6 = 60
• 7 ⋅ 10 = 10 ⋅ 7 = 70
• 8 ⋅ 10 = 10 ⋅ 8 = 80
• 9 ⋅ 10 = 10 ⋅ 9 = 90
• 10 ⋅ 10 = 10 ⋅ 10 = 100