ווי צו געשווינד און לייכט לערנען די קייפל טיש

קייפל איז א מאטעמאטישע אפעראציע וואס קען רעפרעזענטירט ווערן אלס א סומע פון ​​יידענישע ווערטער.

אַלגעמיינע פּרינציפּ פון קייפל

פֿאַר בייַשפּיל, די אַ ⋅ ב (לייענען ווי "אַ מאָל ב") מיטל אַז מיר סאַכאַקל די טערמינען a, די נומער פון וואָס איז גלייַך צו b. דער רעזולטאַט פון אַ קייפל איז גערופן אַ פּראָדוקט.

ביישפילן:

• 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12

  (זעקס מאל צוויי)

• 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20

  (פיר מאל פינף)

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

  (אכט מאל דריי)

ווי מיר וויסן, פון די פּערמיוטיישאַן פון די ערטער פון די סיבות, די פּראָדוקט טוט נישט טוישן. פֿאַר די ביישפילן אויבן, עס טורנס אויס:

• 6 ⋅ 2 = 6 + 6 = 12

  (צוויי מאל זעקס)

• 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20

  (פינף מאל פיר)

• 8 ⋅ 3 = 8 + 8 + 8 = 24

  (דרײַ מאָל אַכט)

פּראַקטיש בענעפיץ

דאַנק צו קייפל, איר קענען באטייטיק רעדוצירן די ציילן פון די גאַנץ נומער פון זאכן פון די זעלבע טיפּ, אאז"ו ו. פֿאַר בייַשפּיל, אויב מיר האָבן 7 פּאַקאַדזשאַז, יעדער פון וואָס כּולל 5 פּענס, די גאַנץ נומער פון פּענס איז געפֿונען דורך מאַלטאַפּלייינג די. צוויי נומערן:

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

(פינף פּענס זיבן מאל)

מערן מיט 0

דער רעזולטאַט איז שטענדיק נול.

• 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

מערן מיט 1

דער פּראָדוקט איז גלייַך צו אן אנדער מאַלטאַפּלייער ווי איין.

• 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

מערן מיט 2

לייג דער ערשטער פאַקטאָר צו זיך.

• 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

מערן מיט 3

מיר מערן דער ערשטער פאַקטאָר מיט 2, און לייגן עס צו דער רעזולטאַט.

• 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

מערן מיט 4

מיר לייגן די זעלבע סומע צו די דאַבאַלד ערשטער פאַקטאָר.

• 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

מערן מיט 5

אויב די אנדערע מאַלטאַפּלייער איז אַן אפילו נומער, דער רעזולטאַט וועט סוף אין נול, אויב מאָדנע, אין די נומער 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

מערן מיט 6

מיר מערן דער ערשטער פאַקטאָר מיט 5, און לייגן די רעזולטאַט צו עס.

• 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

מערן מיט 7

עס איז קיין סימפּלאַפייד אַלגערידאַם פֿאַר מאַלטאַפּלייינג מיט 7, אַזוי מיר נוצן מעטהאָדס אָנווענדלעך צו אנדערע סיבות.

• 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

מערן מיט 8

מיר מערן דער ערשטער פאַקטאָר מיט 4, און לייגן די זעלבע סומע צו דער רעזולטאַט.

• 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

מערן מיט 9

מיר מערן דער ערשטער פאַקטאָר מיט 10, און דאַן אַראָפּרעכענען עס פון דער רעזולטאַט.

• 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

מערן מיט 10

לייג נול צו די סוף פון די אנדערע מאַלטאַפּלייער.

• 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