كيف تتعلم جدول الضرب بسرعة وسهولة

تضاعف هي عملية حسابية يمكن تمثيلها كمجموع من المصطلحات المتطابقة.

مبدأ الضرب العام

على سبيل المثال، أ ⋅ ب (يُقرأ بعبارة "أ في ب") يعني أننا نجمع المصطلحات a، وعددها يساوي b. تسمى نتيجة الضرب منتجًا.

أمثلة:

• 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

  (ستة ضرب اثنين)

• 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20

  (أربعة ضرب خمسة)

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

  (ثمانية ضرب ثلاثة)

كما نعلم ، من تقليب أماكن العوامل ، لا يتغير المنتج. للأمثلة أعلاه ، اتضح:

• 6 ⋅ 2 = 6 + 6 = 12

  (اثنان ضرب ستة)

• 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20

  (خمسة ضرب أربعة)

• 8 ⋅ 3 = 8 + 8 + 8 = 24

  (ثلاثة ضرب ثمانية)

فوائد عملية

بفضل الضرب ، يمكنك تقليل العدد الإجمالي للعناصر من نفس النوع بشكل كبير ، إلخ. على سبيل المثال ، إذا كان لدينا 7 عبوات ، كل منها تحتوي على 5 أقلام ، فسيتم العثور على العدد الإجمالي للأقلام بضرب هذه رقمين:

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

(خمسة أقلام سبع مرات)

اضرب بواسطة 0

النتيجة دائما صفر.

• 0،0 0 = XNUMX،XNUMX
• 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
• 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

اضرب بواسطة 1

المنتج يساوي مضاعف آخر غير واحد.

• 1،1 1 = XNUMX،XNUMX
• 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

اضرب بواسطة 2

أضف العامل الأول لنفسه.

• 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

اضرب بواسطة 3

نضرب العامل الأول في 2 ، ثم نضيفه إلى النتيجة.

• 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

اضرب بواسطة 4

نضيف نفس المقدار إلى العامل الأول المضاعف.

• 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

اضرب بواسطة 5

إذا كان المضاعف الآخر عددًا زوجيًا ، فستنتهي النتيجة بصفر ، إذا كان عددًا فرديًا ، في الرقم 5.

• 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

اضرب بواسطة 6

نضرب العامل الأول في 5 ، ثم نضيف النتيجة إليه.

• 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

اضرب بواسطة 7

لا توجد خوارزمية مبسطة للضرب في 7 ، لذلك نستخدم طرقًا قابلة للتطبيق على عوامل أخرى.

• 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 = XNUMX،XNUMX

اضرب بواسطة 8

نضرب العامل الأول في 4 ، ثم نضيف المقدار نفسه إلى النتيجة.

• 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

اضرب بواسطة 9

نضرب العامل الأول في 10 ، ثم نطرحه من النتيجة التي تم الحصول عليها.

• 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

اضرب بواسطة 10

أضف صفرًا إلى نهاية المضاعف الآخر.

• 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