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{懂教孩子的便應這樣教} 九因歌 VS 印式口訣

21/8/2014

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所有在傳統中國 (包括香港) 社會長大的人仕,十之八九應曾朗誦九因歌,什麼一一如一,二二如四等乘數口訣。根據維基百科 (連結) 所述,九因歌,亦叫乘數表或者乘法口訣,係十進制乘數表,可以幫手計簡單乘、除同開方。佢係中國發明,現時文獻所示,春秋戰國用到依家,歷代只係字句同次序稍有唔同。完整嘅九因歌有乘式八十一項,唔計重覆嘅,就有四十五項。九因歌如下圖所構成 : 
图片
九因歌,陪伴著小弟成長,應付著日常的數學運算,幫助甚大,但很多時,總有一種感覺便是不能計算大數,雙位數的運算,難以靈活處理,克板阻礙,而且,讓人有種強記背誦的感覺。最近閱報 (連結),介紹了印度乘數表,其運算方式讓小弟讚嘆,當中最重要的是其利用科學的方法,把困難問題簡單化而不失精準,實值得推介,取長補短。

據介紹,印度乘數表已延伸到「19」,相信曾背誦九因歌的朋友,應知雙位數的乘法較單位數乘法複雜得多,但聰明的印度人想出一個有效的心算方法,化繁為簡,詳述如下 :
图片
首先將被乘數,與乘數的個位相加,然後將之乘十;把被乘數的個位數與乘數的個位數相乘,最後把兩組數加起來便得出答案。

印度乘法例子 : 例如:13×12=?(13是被乘數;12是乘數)

印度人是這樣算的:

第一步:把(13)跟乘數的個位數(2)加起來13+2=15
第二步:把第一步的答案乘以10 15×10=150
第三步:把被乘數的個位數(3)乘以乘數的個位數(2) 2X3=6
第四步:第二步+第三步 150+6=156

總算法:(13+2)×10+(2X3)=156



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