כיצד ללמוד במהירות ובקלות את לוח הכפל

תוכן

העיקרון הכללי של הכפל
הכפל ב 0
הכפל ב 1
הכפל ב 2
הכפל ב 3
הכפל ב 4
הכפל ב 5
הכפל ב 6
הכפל ב 7
הכפל ב 8
הכפל ב 9
הכפל ב 10

כפל היא פעולה מתמטית שניתן לייצג אותה כסכום של מונחים זהים.

תוֹכֶן

העיקרון הכללי של הכפל

לדוגמה, a ⋅ ב (קרא כ"א כפול ב") פירושו שאנו מסכמים את המונחים a, שמספרם שווה ל b. התוצאה של הכפל נקראת מכפלה.

דוגמאות:

2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12
(שש כפול שתיים)
5 ⋅ 4 = 5 + 5 + 5 + 5 = 20
(ארבע כפול חמש)
3 ⋅ 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24
(שמונה כפול שלוש)

כידוע, מהתמורה של מקומות הגורמים, התוצר לא משתנה. לגבי הדוגמאות לעיל, מסתבר:

6 ⋅ 2 = 6 + 6 = 12
(פעמיים שש)
4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20
(חמש כפול ארבע)
8 ⋅ 3 = 8 + 8 + 8 = 24
(שלוש פעמים שמונה)

יתרונות מעשיים

הודות להכפלה, ניתן לצמצם משמעותית את ספירת הפריטים הכוללים מאותו סוג וכו'. לדוגמה, אם יש לנו 7 אריזות שכל אחת מהן מכילה 5 עטים, אזי מוצאים את המספר הכולל של עטים על ידי הכפלה של אלה. שני מספרים:

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

(חמישה עטים שבע פעמים)

הכפל ב 0

התוצאה תמיד אפס.

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

הכפל ב 1

המכפלה שווה למכפיל אחר מלבד אחד.

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

הכפל ב 2

הוסף את הגורם הראשון לעצמו.

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

הכפל ב 3

נכפיל את הגורם הראשון ב-2, ואז נוסיף אותו לתוצאה.

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

הכפל ב 4

נוסיף את אותה כמות לגורם הראשון הכפול.

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

הכפל ב 5

אם המכפיל השני הוא מספר זוגי, התוצאה תסתיים באפס, אם אי זוגי, במספר 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

הכפל ב 6

נכפיל את הגורם הראשון ב-5, ואז נוסיף לו את התוצאה.

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

הכפל ב 7

אין אלגוריתם פשוט להכפלה ב-7, ולכן אנו משתמשים בשיטות החלות על גורמים אחרים.

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

הכפל ב 8

נכפיל את הגורם הראשון ב-4, ואז נוסיף את אותה כמות לתוצאה.

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

הכפל ב 9

נכפיל את הגורם הראשון ב-10, ואז נחסר אותו מהתוצאה המתקבלת.

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

הכפל ב 10

הוסף אפס לסוף המכפיל השני.

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