分数这个词来自拉丁语“broken”,即“分开”的意思。那时的分数是比1小的数,是把1分成更小的部分。如今我们使用分数的方法始于400年前,在人们还为分数是否是数争论不休的时候就开始了。
参加过生日宴会的人都知道分数:一个蛋糕该切几块?如果有两位宾客,就切成两半——尽管有点贪吃呢。4位宾客就各拿1/4,12位宾客就各拿1/12。人再多的话可能得再来一个蛋糕了。尽管数学界对分数直到17世纪才统一意见,但古人显然懂得数(或者蛋糕)是可以分成好几部分(块)的。
眼与口
古埃及人首先发明了书写分数的办法。荷鲁斯之眼源自鹰头天神荷鲁斯,是古埃及的一个符号。其中眼睛表示1,它的各部分进行了划分(见左图),用于分割谷物、面粉及其他有价作物。分数的另一种写法是在一个嘴的形状下面写个数。嘴表示1,下面的数表示分成了几块。这套系统可以表示任意分数,它们被称为单位分数,分子是1。1/2、1/5、1/23都是单位分数,2/3、3/7、9/23不是。
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荷鲁斯之眼,源自古埃及鹰头天神的符号,被分成了几部分,用于表示对食物和饮用水等的划分。
分子与分母
我们把分数写成两个数,一个在上,一个在下。底下的是分母,表示1分成多少份。上面的是分子,表示在这个分数里占了多少份。这个想法来自公元7世纪的印度,阿拉伯学者随后在两个数之间加一横杠,分数的意义就更明确了。
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编制分数表
古埃及数学里不许可非单位分数出现。于是四分之三,或者说3/4,分成了单位分数1/2+1/4。单位分数的重复叠加也不许可,所以把2/11变成1/11+1/11也是不行的。古埃及数学家编制了一份分数表,把众多分数转化成他们许可使用的单位分数。这个规则把事情变得复杂了。在古埃及的宴会.上把3块糕点分给5个客人,意味着每个客人各得到3小块:一块1/3的,一-块1/5的,最后是一块1/15的。