गुणाकार सारणी पटकन आणि सहज कशी शिकायची

गुणाकार हे एक गणितीय ऑपरेशन आहे ज्याला समान संज्ञांची बेरीज म्हणून प्रस्तुत केले जाऊ शकते.

गुणाकाराचे सामान्य तत्व

उदाहरणार्थ, अगोदर निर्देश केलेल्या बाबीसंबंधी बोलताना a ⋅ b (“a times b” म्हणून वाचा) म्हणजे आपण अटींची बेरीज करतो a, ज्याची संख्या समान आहे b. गुणाकाराच्या परिणामास उत्पादन म्हणतात.

उदाहरणे:

• २ ⋅ ६ = २ + २ + २ + २ + २ + २ = १२

  (सहा वेळा दोन)

• ५ ⋅ ४ = ५ + ५ + ५ + ५ = २०

  (चार वेळा पाच)

• ३ ⋅ ८ = ३ + ३ + ३ + ३ + ३ + ३ + ३ + ३ = २४

  (आठ वेळा तीन)

आपल्याला माहित आहे की, घटकांच्या स्थानांच्या क्रमपरिवर्तनातून, उत्पादन बदलत नाही. वरील उदाहरणांसाठी, हे बाहेर वळते:

• ६ ⋅ २ = ६ + ६ = १२

  (दोन वेळा सहा)

• ४ ⋅ ५ = ४ + ४ + ४ + ४ + ४ = २०

  (पाच वेळा चार)

• 8 ⋅ 3 = 8 + 8 + 8 = 24

  (तीन वेळा आठ)

व्यावहारिक लाभ

गुणाकार केल्याबद्दल धन्यवाद, तुम्ही समान प्रकारच्या वस्तूंच्या एकूण संख्येची संख्या लक्षणीयरीत्या कमी करू शकता, इ. उदाहरणार्थ, जर आमच्याकडे 7 पॅकेजेस असतील, ज्यामध्ये प्रत्येकामध्ये 5 पेन असतील, तर त्यांचा गुणाकार करून एकूण पेनची संख्या सापडेल. दोन संख्या:

५ ⋅ ७ = ५ + ५ + ५ + ५ + ५ + ५ + ५ = ३५

(पाच पेन सात वेळा)

0 ने गुणाकार करा

परिणाम नेहमीच शून्य असतो.

• ३,६७ ⋅ १० = ३६,७
• 1 ⋅ 0 = 0 ⋅ 1 = 0
• 2 ⋅ 0 = 0 ⋅ 2 = 0 + 0 = 0
• ३ ⋅ ० = ० ⋅ ३ = ० + ० + ० = ०
• ४ ⋅ ० = ० ⋅ ४ = ० + ० + ० + ० = ०
• 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 ने गुणाकार करा

उत्पादन हे एका व्यतिरिक्त दुसर्‍या गुणकाच्या बरोबरीचे आहे.

• ३,६७ ⋅ १० = ३६,७
• 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 ने गुणाकार करा

प्रथम घटक स्वतःमध्ये जोडा.

• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२
• ६ ⋅ २ = ६ + ६ = १२

3 ने गुणाकार करा

आम्ही पहिला घटक 2 ने गुणाकार करतो, नंतर तो निकालात जोडा.

• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३

4 ने गुणाकार करा

आम्ही दुप्पट पहिल्या घटकामध्ये समान रक्कम जोडतो.

• 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 ने गुणाकार करा

जर दुसरा गुणक सम संख्या असेल, तर परिणाम शून्यात, विषम असल्यास, 5 मध्ये संपेल.

• 1 ⋅ 5 = 5 ⋅ 1 = 5
• 2 ⋅ 5 = 5 ⋅ 2 = 5 + 5 = 10
• ३ ⋅ ५ = ५ ⋅ ३ = (५ ⋅ २) + ५ = १५
• 4 ⋅ 5 = 5 ⋅ 4 = (5 ⋅ 2) + (5 ⋅ 2) = 20
• ४ ⋅ ५ = ४ + ४ + ४ + ४ + ४ = २०
• ३ ⋅ ५ = ५ ⋅ ३ = (५ ⋅ २) + ५ = १५
• 7 ⋅ 5 = 5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
• 8 ⋅ 5 = 5 ⋅ 8 = (5 ⋅ 4) + (5 ⋅ 4) = 40
• ९ ⋅ ५ = ५ ⋅ ९ = (५ ⋅ १०) – ५ = ४५
• 10 ⋅ 5 = 5 ⋅ 10 = 50

6 ने गुणाकार करा

आम्ही पहिला घटक 5 ने गुणाकार करतो, नंतर त्यात परिणाम जोडा.

• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३
• १ ⋅ ३ = (१ ⋅ २) + १ = २ + १ = ३

7 ने गुणाकार करा

7 ने गुणाकार करण्यासाठी कोणतेही सरलीकृत अल्गोरिदम नाही, म्हणून आम्ही इतर घटकांना लागू असलेल्या पद्धती वापरतो.

• 1 ⋅ 7 = 7 ⋅ 1 = 7
• 2 ⋅ 7 = 7 ⋅ 2 = 7 + 7 = 14
• ३ ⋅ ५ = ५ ⋅ ३ = (५ ⋅ २) + ५ = १५
• 4 ⋅ 7 = 7 ⋅ 4 = (7 ⋅ 2) + (7 ⋅ 2) = 28
• 5 ⋅ 7 = 7 ⋅ 5 = 7 + 7 + 7 + 7 + 7 = 35
• ३ ⋅ ५ = ५ ⋅ ३ = (५ ⋅ २) + ५ = १५
• ५ ⋅ ७ = ५ + ५ + ५ + ५ + ५ + ५ + ५ = ३५
• 8 ⋅ 7 = 7 ⋅ 8 = (7 ⋅ 4) + (7 ⋅ 4) = 56
• ९ ⋅ ५ = ५ ⋅ ९ = (५ ⋅ १०) – ५ = ४५
• ३,६७ ⋅ १० = ३६,७

8 ने गुणाकार करा

आम्ही पहिला घटक 4 ने गुणाकार करतो, नंतर परिणामात समान रक्कम जोडतो.

• 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 ने गुणाकार करा

आम्ही पहिल्या घटकास 10 ने गुणाकार करतो आणि नंतर प्राप्त झालेल्या निकालातून वजा करतो.

• 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 ने गुणाकार करा

दुसऱ्या गुणकाच्या शेवटी शून्य जोडा.

• 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