SỐ HỌC ẤN ĐỘ: BẢNG “THẬP CỬU CHƯƠNG”

Khi các bà mẹ Việt Nam đang vui mừng vì con mình học thuộc được bảng cửu chương 9x9 thì trẻ em Ấn Độ đã học nằm lòng phép nhân 19x19 rồi. C...

Khi các bà mẹ Việt Nam đang vui mừng vì con mình học thuộc được bảng cửu chương 9x9 thì trẻ em Ấn Độ đã học nằm lòng phép nhân 19x19 rồi. Chẳng trách những năm gần đây Ấn Độ phát triển nhanh như vậy…
“Bảng cửu chương” của Ấn Độ được tính từ 1 đến 19 (có lẽ là “Bảng thập cửu chương” thì đúng hơn). Nhưng các bạn có biết người Ấn Độ ghi nhớ các con số từ 11  đến 19 như thế nào không ?
Ở bài này, Dattenhay.vn xin giới thiệu “Bảng thập cửu chương” của Ấn Độ, các bạn đừng bỏ lỡ, bởi vì nó quả thực kỳ thú!


Chúng ta hãy thử tính đáp án của phép nhân sau: 13 x 12 = ?
Ta gọi số thứ nhất (13) là số bị nhân, số thứ hai (12) là số nhân. Người Ấn Độ tính phép nhân này như sau:
Bước 1: Lấy số bị nhân 13 cộng với số hàng đơn vị của số nhân là 2: 13+2=15.
Bước 2: Lấy đáp án ở bước thứ nhất nhân với 10 (cũng có nghĩa là sau con số đáp án thêm số 0 vào): 15x10=150.
Bước 3: Lấy số hàng đơn vị của số bị nhân là 3 nhân với số hàng đơn vị của số nhân là 2:3x2=6.
Bước 4: Lấy kết quả ở Bước 2 cộng với kết quả ở Bước 3 sẽ ra đáp án cuối cùng: (13+2)10 + 6 = 156.
Với cách làm như vậy, chỉ cần để ý một chút là chúng ta có thể nhanh chóng tính ra đáp án của các phép tính từ 11x11 đến 19x19 rồi đấy. 
Chúng ta hãy thử làm thêm các phép tính sau xem sao:

14x13= ?
16x17= ?
19x19= ?
Bước 1
14+3=17
16+7=23
19+9=28
Bước 2
17x10=170
23x10=230
28x10=280
Bước 3
4x3=12
6x7=42
9x9=81
Bước 4
170+12=182
230+42=272
280+81=361
Đây là phép tính nhẩm đơn giản, chủ yếu là dạy cho học sinh cấp 1. Còn các bậc phụ huynh thì ngoài việc biết cách nhân nhẩm nhanh này ra thì cũng nên hiểu thêm một chút về nguyên lý của nó. Dưới đây là sơ đồ biểu diễn cách tính độc đáo này thông qua hình học phẳng.
Vẽ một hình chữ nhật có chiều dài 13 và chiều rộng 12 (không cần tính đến đơn vị đo, chỉ cần tỷ lệ tương đối là được). Men theo các cạnh của hình chữ nhật vẽ hình vuông với độ dài các cạnh là 10. Như hình vẽ biểu thị, khi chúng ta chuyển hình chữ nhật bị bôi xanh sang vị trí mới (theo hình mũi tên) thì hình chữ nhật ban đầu với kích thước 13 x 12 sẽ biến thành một hình vẽ mới có hai phần: một hình chữ nhật lớn có kích thước 15 x 10 và một hình chữ nhật nhỏ có kích thước 3 x 2. Như vậy, diện tích hình vẽ mới là bằng tổng diện tích của hai hình chữ nhật lớn nhỏ.

Diện tích hình chữ nhật lớn là 15 x 10 = 150    --- Tương ứng với Bước 1 và Bước 2.
Diện tích hình chữ nhật nhỏ là 3 x 2 = 6          --- Tương ứng với Bước 3.
Diện tích hình vẽ mới là          150 + 6 = 156   --- Tương ứng với Bước 4.

Cách tính phép nhân này còn có một kiểu khác có tính chất tổng quát như sau:
Bước 1: Tính tích của cả số hàng chục của số nhân và số bị nhân. Nói ra thì dài dòng, thực chất ở đây là 10 x 10 = 100.
Bước 2: Tính tổng của các số hàng đơn vị rồi nhân với 10.
Bước 3: Các số hàng đơn vị nhân với nhau.
Bước 4: Cộng kết quả của cả 3 bước lại sẽ ra đáp án cuối cùng.

Trở lại ví dụ đầu tiên, chúng ta tính lại phép tính: 13 x 12 = ?
Bước 1: 10 x 10 = 100 (bạn đừng có làm phép nhân 1 x 1 đấy!).
Bước 2: (3 + 2) x 10 = 50.
Bước 3: 3 x 2 = 6.
Bước 4: 100 + 50 + 6 = 156.
Dưới đây là 3 ví dụ nữa:

15x17= ?
14x18= ?
19x13= ?
Bước 1
10 x 10 = 100
10 x 10 = 100
10 x 10 = 100
Bước 2
(5+7) x 10 = 120
(4+8) x 10=120
(9+3) x 10= 120
Bước 3
5 x 7 = 35
4 x 8=32
9 x 3= 27
Bước 4
100+120+35=255
100+120+32=252
100+120+21=247
Nguyên lý của phương pháp này như sau:
Vẽ hình chữ nhật có kích thước 15 x 17 thành bốn phần A, B, C, D như hình dưới đây. Diện tích của bài toán chính là tổng diện tích của bốn phần này.

                          

Diện tích hình vuông A là 10 x 10 = 100                           --- Tương ứng với Bước 1.
Tổng diện tích hình chữ nhật B và C là (5+7)x10 = 120     --- Tương ứng với Bước 2.
Diện tích của hình chữ nhật D là 5 x 7 = 35                       --- Tương ứng với Bước 3.
Diện tích của cả hình chữ nhật lớn là 100+120+35 = 255    --- Tương ứng với Bước 4.
Nói là làm 4 bước xem ra có vẻ lâu, nhưng thực ra chia nhỏ các phép tính và tính nhẩm trong đầu cũng rất nhanh. Nhìn lướt qua là đã tính được 3 bước đầu rồi, chỉ có phép cộng cuối cùng (tùy theo phép tính) thì có lẽ hơi lâu một chút xíu. Nếu thực hành quen rồi thì thời gian cho mỗi phép tính trong phạm vi nói trên có lẽ không quá 10 giây. Quả thực là rất thú vị phải không các bạn?

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Lê Ngân: SỐ HỌC ẤN ĐỘ: BẢNG “THẬP CỬU CHƯƠNG”
SỐ HỌC ẤN ĐỘ: BẢNG “THẬP CỬU CHƯƠNG”
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FK/X6gArjLL9nD4eaZ46n8U23gLwZb+Jrr/AF2rx6JbJfy/d+9OE8w/dXqf4R6CuzoqJ04TtzJO3c6cPjcRh1JUKkocys7Nq67O268mFFFFWcwV/MN/wVn/AOVkr9oj/sBaN/6ZtEr+nmv5hv8AgrP/AMrJX7RH/YC0b/0zaJX1nAv/ACP8L/jX5M+Q4/8A+Sexf+D9Uc5RRRX9gH8ZBXk/7cX/ACa54o/7dP8A0rhr1ivJ/wBuL/k1zxR/26f+lcNeFxT/AMiXGf8AXqp/6Qz6DhT/AJHeD/6+0/8A0tH9Ov8AwSd/5RZfs0/9kq8L/wDpota9/rwD/gk7/wAosv2af+yVeF//AE0Wte/1/GB/bgUUV81ftk/8FFJP2Z9fuPD/AIT+F3xA+LfiaxtRd6hb+HtPmkstIVhujW6uUjk8p3X5goRiFwxwGXPNi8ZRw1N1azsvm/uSu38j28g4dzDO8YsBllPnqPW14xSXeUpOMYq7SvJpXaW7R9K0V83/APBPL/gpp4L/AOCiPh7WX0Gw1PQNf8OGI6jpV/tdkjkB2SxyL8skZZWXorAryoDKW+kKeExlHFUlXw8lKL2aFxDw9mWRZhUyvN6LpV6dlKMt1dJra6aaaaabTTumeAf8FYv+UWX7S3/ZKvFH/pouq/ll/Y91r4+2n7Ofh2PwV+038YPh74ZX7T9j8P6Jr+o2thYf6VN5nlxw3cca75N8h2oMtIxOSST/AFNf8FYv+UWX7S3/AGSrxR/6aLqv5iv2Hf8Ak1zwv/29/wDpXNX6X4a5Hgc1zOph8fDngqbkldrVSir3i09m/I/HvE/P8flOVU8Tl9Tkm6ii3aL0cZu1pJrdLzOn/wCEj/an/wCjzv2gP/Cq1f8A+T6P+Ej/AGp/+jzv2gP/AAqtX/8Ak+uxor9u/wCIacN/9A3/AJPU/wDkz8J/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Po/4SP8Aan/6PO/aA/8ACq1f/wCT67Gij/iGnDf/AEDf+T1P/kw/4ijxP/0Ff+SU/wD5A47/AISP9qf/AKPO/aA/8KrV/wD5Pr7b/wCCK37C3jv9pi4+KF54a+Ofi34a+JLNtMm8T65pkVw1941u5jek3d7JHdwvLKJEmfdK0rFrmQ5BLFvlWv1C/wCDZD/j6+On+/oX89Sr5ri/hzLchyqrjMrpKFT3Vd3n9qK2m5Lr2P2fwd4yzfM6mN+v1efkhFx92Cs3NJ7RXTueqf8ADnj45/8AR63xY/796h/8s6P+HPHxz/6PW+LH/fvUP/lnX6DUV+K/61Zl/NH/AMF0/wD5E/aP7WxPdf8AgMf8j8+f+HPHxz/6PW+LH/fvUP8A5Z0f8OePjn/0et8WP+/eof8Ayzr9BqKP9asy/mj/AOC6f/yIf2tie6/8Bj/kfnz/AMOePjn/ANHrfFj/AL96h/8ALOj/AIc8fHP/AKPW+LH/AH71D/5Z1+g1FH+tWZfzR/8ABdP/AORD+1sT3X/gMf8AI/GP/gr/AP8ABJH4reH/APgnX8Q7zxL+1d8QvGuiw/2b9p0bU7a8ltbzOp2gXesmoOp2OVcZU8oOhwR+mP8AwTV8N/8ACG/8E5vgBo/n/af7J+G/h2z87Zs83y9Mt03bcnGcZxk4z1Ned/8ABcH/AJRefE//ALhX/p2sq9Y/YM/5Ma+DH/Yi6J/6b4K0zGrLF5bDHV7Op7Rwuko+6oxaVopLdvW1+l7JDxM3Ww0a9T4uZq9ktEk9lZbt+Z6vRRRXzJ5gV81f8FYvGq+Fv2PtSsTIEl8Q6ha2CDu22Tz2/DEJ/P3r6Vr87P8Agsv8UP8AhI/ib4U8E2bmZtHtmvbmNOSZp2CxoR/eCJke0tfCeJeaLA8OYmV9ZrkXm56P/wAlu/kfdeG2WPG8RYaNtIPnfkoar8bL5nuP/BInwefDn7JS37IQ2v6vc3gYjllXZAPwzC35mvqKuQ+AHw2X4P8AwS8LeGQqq+jabDbzbejTbQZW/GQsfxrr697hjLXl+UYbBS3hCKfrbX8bnhcT5ksfm2Jxkdpzk16X0/CwUUUV7p4QUUUUAFFFFABRRRQB4B/wVH/YY/4eUfsJ+Ovgp/wlP/CF/wDCafYP+Jz/AGb/AGj9j+y6hbXv+o82Lfu+z7P9YuN+7nG0/nh4T/4NmP2kvAXhXTNC0L/gpN8cNF0TRbSKw0/T7Cx1S2tLC3iQJFDFEmthI40RVVUUAKAAAAK/Y6igD8gf+IcT9qf/AKSc/tAf9+dX/wDl5R/xDiftT/8ASTn9oD/vzq//AMvK/X6igD8gf+IcT9qf/pJz+0B/351f/wCXlH/EOJ+1P/0k5/aA/wC/Or//AC8r9fqKAPyB/wCIcT9qf/pJz+0B/wB+dX/+XlH/ABDiftT/APSTn9oD/vzq/wD8vK/X6igD8gf+IcT9qf8A6Sc/tAf9+dX/APl5R/xDiftT/wDSTn9oD/vzq/8A8vK/X6igD8gf+IcT9qf/AKSc/tAf9+dX/wDl5R/xDiftT/8ASTn9oD/vzq//AMvK/X6igD8gf+IcT9qf/pJz+0B/351f/wCXlH/EOJ+1P/0k5/aA/wC/Or//AC8r9fqKAPyB/wCIcT9qf/pJz+0B/wB+dX/+XlH/ABDiftT/APSTn9oD/vzq/wD8vK/X6igD8gf+IcT9qf8A6Sc/tAf9+dX/APl5R/xDiftT/wDSTn9oD/vzq/8A8vK/X6igD8gf+IcT9qf/AKSc/tAf9+dX/wDl5R/xDiftT/8ASTn9oD/vzq//AMvK/X6igD8gf+IcT9qf/pJz+0B/351f/wCXlH/EOJ+1P/0k5/aA/wC/Or//AC8r9fqKAPyB/wCIcT9qf/pJz+0B/wB+dX/+XlH/ABDiftT/APSTn9oD/vzq/wD8vK/X6igD8gf+IcT9qf8A6Sc/tAf9+dX/APl5R/xDiftT/wDSTn9oD/vzq/8A8vK/X6vLf2q/2qtO/ZZ8H2d7L4f8U+M9d1eZoNK8PeG9Pe+1LUmUAyMsa/djjUgu54GVHLMqnKvXhRg6lR2SO/LMsxWY4qGCwUHOpN2SX37uySSu220kk22kj80/+IcT9qf/AKSc/tAf9+dX/wDl5R/xDiftT/8ASTn9oD/vzq//AMvK+q/2R/8Ags9oH7Qn7RI+FHjDwB4q+Fnjm5eSO0stXzIsrqnmLDJujjkhleL5wrx7TjAckru+06wwOY4fGU3Uw0uZJ2e6s10admn6nr8VcH5xw3i44LOqDpTlFTjrGSlF3tKMouUZRdnrFtaH4Ufsqf8ABLT4g6D/AMFQfiN8Mz+0b4ym+J3hzwul5q/xU+yXK694mt3GmyJaXD/bTOY0W4t0Ae5kGLKLCgBQn2j/AMOePjn/ANHrfFj/AL96h/8ALOj9nb/lYo+PX/Yi2v8A6I0Kv0Gr9DzXOsXg1Qo4dxUfZU38EHq4q7u4t/icuLx1Wj7OFOyXJF/DF9PNH58/8OePjn/0et8WP+/eof8Ayzo/4c8fHP8A6PW+LH/fvUP/AJZ1+g1FeV/rVmX80f8AwXT/APkTl/tbE91/4DH/ACPz5/4c8fHP/o9b4sf9+9Q/+WdH/Dnj45/9HrfFj/v3qH/yzr9BqKP9asy/mj/4Lp//ACIf2tie6/8AAY/5H58/8OePjn/0et8WP+/eof8Ayzr88dO/4ItfFv4q/wDBbD4w+HPD37X3xG8DeNrHwva3l/4206zvRqur24t9JAtJXTUo5TH+8h4aVh/o0fy8Db/QpX58/s7f8rFHx6/7EW1/9EaFXZhswrZlQxEMZaShTc42jGNpKUUneKTekno7ryukbU8RPE06ka1nyxutEtbpdEujemx4P/xDiftT/wDSTn9oD/vzq/8A8vKP+IcT9qf/AKSc/tAf9+dX/wDl5X6/UV8ieOfkD/xDiftT/wDSTn9oD/vzq/8A8vK5/wCKX/BrZ8ffjj4Ev/C3jb/gon8YPGHhnVPL+2aRrek6jqFhd+XIssfmQTa00b7ZERxuBwyKRyAa/Z6igDgP2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