Yaliyomo
Kuzidisha ni operesheni ya hisabati inayoweza kuwakilishwa kama jumla ya istilahi zinazofanana.
Kanuni ya jumla ya kuzidisha
Kwa mfano, a ⋅ b (soma kama "nyakati b") inamaanisha kwamba tunajumlisha maneno a, idadi ambayo ni sawa na b. Matokeo ya kuzidisha inaitwa bidhaa.
mifano:
- 2 ⋅ 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12
(sita mara mbili)
- 5 ⋅ 4 = 5 + 5 + 5 + 5 = 20
(nne mara tano)
- 3 ⋅ 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24
(nane mara tatu)
Kama tunavyojua, kutoka kwa idhini ya maeneo ya mambo, bidhaa haibadilika. Kwa mifano hapo juu, inageuka:
- 6 ⋅ 2 = 6 + 6 = 12
(mbili mara sita)
- 4 ⋅ 5 = 4 + 4 + 4 + 4 + 4 = 20
(tano mara nne)
- 8 ⋅ 3 = 8 + 8 + 8 = 24
(mara tatu mara nane)
Faida ya vitendo
Shukrani kwa kuzidisha, unaweza kupunguza kwa kiasi kikubwa hesabu ya jumla ya idadi ya vitu vya aina moja, nk Kwa mfano, ikiwa tuna paket 7, ambayo kila moja ina kalamu 5, basi jumla ya kalamu hupatikana kwa kuzidisha hizi. nambari mbili:
5 ⋅ 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
(kalamu tano mara saba)
Zidisha kwa 0
Matokeo yake daima ni sifuri.
- 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
Zidisha kwa 1
Bidhaa ni sawa na kizidishi kingine isipokuwa kimoja.
- 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
Zidisha kwa 2
Ongeza sababu ya kwanza yenyewe.
- 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
Zidisha kwa 3
Tunazidisha kipengele cha kwanza kwa 2, kisha uongeze kwenye matokeo.
- 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
Zidisha kwa 4
Tunaongeza kiasi sawa kwa sababu ya kwanza mara mbili.
- 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
Zidisha kwa 5
Ikiwa kizidishi kingine ni nambari sawa, matokeo yataisha kwa sifuri, ikiwa isiyo ya kawaida, katika nambari 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
Zidisha kwa 6
Tunazidisha sababu ya kwanza kwa 5, kisha ongeza matokeo kwake.
- 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
Zidisha kwa 7
Hakuna algoriti iliyorahisishwa ya kuzidisha kwa 7, kwa hivyo tunatumia mbinu zinazotumika kwa vipengele vingine.
- 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
Zidisha kwa 8
Tunazidisha kipengele cha kwanza kwa 4, kisha kuongeza kiasi sawa kwa matokeo.
- 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
Zidisha kwa 9
Tunazidisha sababu ya kwanza kwa 10, na kisha kuiondoa kutoka kwa matokeo yaliyopatikana.
- 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
Zidisha kwa 10
Ongeza sifuri hadi mwisho wa kizidishi kingine.
- 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