q1 So let me just rewrite that as, I just want to divide by q1 everywhere.

分子分母同时除以，现在我写的这些。

麻省理工公开课 - 热力学与动力学课程节选

But here I'm doing the exact same thing except my number here 13 0 in the bottom in the denominator is 13.0.

但是这里我在做一个同样的计算,除了在下面的分母是。

哈佛公开课 - 计算机科学课程节选

If they both go up by the same proportion, then numerator and denominator go up by the same amount, so there's no change.

如果大家都上升了相同幅度,分子和分母同比例增大,则没有变化

耶鲁公开课 - 金融市场课程节选

And I've reversed the fraction here because of the negative sign here.

我交换了分子和分母,因为这里有个负号。

麻省理工公开课 - 热力学与动力学课程节选

Then, I bring the elephant and I pull the spring by the same amount and I find the acceleration of the elephant and the denominator is obviously the mass of the elephant.

然后我再找来大象,用相同的力去拉弹簧,大象就具有了加速度,很明显,分母就是大象的质量

耶鲁公开课 - 基础物理课程节选

Now, of course, there are denominator issues here because we started with a much higher base rate than these other countries, but if you think about the size of the populations there, the number of people who are going to become diabetic in the next twenty-five years is really very frightening.

现在,当然这里存在着分母的问题,我国的增长基数比其他国家要大得多,因为一旦考虑到人口总量,在未来25年成为糖尿病人的人数,就非常非常的惊人了

耶鲁公开课 - 关于食物的心理学、生物学和政治学课程节选

So, the point is whenever you have derivatives with something over dt, do not hesitate to cancel the dts This will be actually true as long as both quantities are vanishingly small.

关键在于,只要你推出的式子分母上有dt,不要犹豫,直接约掉,这个式子只在,两遍都是无穷小的情况下成立

耶鲁公开课 - 基础物理课程节选