乘法 是一种数学运算,可以表示为相同项的总和。
内容
乘法的一般原理
例如 一个 · 乙 (读作“a乘以b”)意味着我们将这些术语相加 a, 其中的数量等于 b. 乘法的结果称为乘积。
例子:
- 2 × 6 = 2 + 2 + 2 + 2 + 2 + 2 = 12
(六乘二)
- 5 × 4 = 5 + 5 + 5 + 5 = 20
(四乘五)
- 3 × 8 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 24
(八乘三)
众所周知,从因素的位置排列来看,乘积是不变的。 对于上面的例子,结果是:
- 6 × 2 = 6 + 6 = 12
(二乘六)
- 4 × 5 = 4 + 4 + 4 + 4 + 4 = 20
(五乘四)
- 8 × 3 = 8 + 8 + 8 = 24
(三乘八)
实际好处
多亏了乘法,你可以显着减少相同类型物品的总数等。例如,如果我们有 7 个包裹,每个包裹包含 5 支钢笔,那么这些钢笔的总数乘以这些两个数字:
5 × 7 = 5 + 5 + 5 + 5 + 5 + 5 + 5 = 35
(五笔七次)
乘以0
结果始终为零。
- 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
乘以1
乘积等于除一以外的另一个乘数。
- 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
乘以2
将第一个因素添加到自身。
- 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
乘以3
我们将第一个因子乘以 2,然后将其添加到结果中。
- 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
乘以4
我们将相同的数量添加到加倍的第一个因素中。
- 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
乘以5
如果另一个乘数是偶数,则结果将以零结尾,如果是奇数,则在数字 5 中。
- 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
乘以6
我们将第一个因子乘以 5,然后将结果添加到其中。
- 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
乘以7
乘以 7 没有简化算法,所以我们使用适用于其他因素的方法。
- 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
乘以8
我们将第一个因子乘以 4,然后将相同的数量添加到结果中。
- 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
乘以9
我们将第一个因子乘以 10,然后从获得的结果中减去它。
- 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
乘以10
将零添加到另一个乘数的末尾。
- 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