数学课上,同学们讨论了“分数乘法”的内容。
小刚提出了一个问题:我看数学书上写着“分数乘分数,用分子相乘的积作分子,用分母相乘的积作分母。”如果按照这个方法计算就是:
, 为什么可以这样计算呢?
小阳:分数乘分数,分母相乘的积决定了分数单位,分子相乘的积决定了分数单位的个数,分数单位和分数单位的个数都确定了,结果也就确定了。
小兵:我觉得可以这样解释:![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3E%EF%BC%88%3C%2Fmi%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3E%EF%BC%89%3C%2Fmi%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmi%3E%EF%BC%88%3C%2Fmi%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3E%EF%BC%89%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3E%EF%BC%88%3C%2Fmi%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E5%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E7%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmi%3E%EF%BC%89%3C%2Fmi%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmi%3E%EF%BC%88%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3Cmi%3E%EF%BC%89%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmrow%3E%3Cmn%3E35%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E6%3C%2Fmn%3E%3Cmrow%3E%3Cmn%3E35%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
小丽:我觉得整数乘法和分数乘法的运算道理是一样的,也可以像小兵那样计算。例如:
30×800=(10×3)×(100×8)=(10×100)×(3×8)=1000×24= 24000
小梅:我觉得小数乘法和分数乘法的运算道理也是一样的。