so I'm going to assume it's true

所以我先假设这是对的
and I'll maybe take a second explaination why it's legitimate.

待会儿再进一步解释为什么合理
What this really means is in a given time,

这里的真正含义是在给定的一段时间内
the change in this quantity is

这个量的变化量等于
a times the change in this quantity.

a乘以这个量的变化量
Therefore, you can multiply both sides by the Δt,

因此你可以两边同时乘以Δt
but the only thing you should understand is Δt,

不过你必须理解这个Δt
as long as it's small and finite,

只要它只是有限小
will lead to some small infinite errors in the formula,

就会在公式中引起无限小的误差
because the formula is really the limit in which Δx and Δt both go to 0.

因为这个式子其实是Δx和Δt同时趋近于0的极限
So what you have to do is multiply both sides by Δt,

那么你要做的只是两边同时乘以Δt
but remember it's got to be in the end made to be vanishingly small.

但请记住 Δt最后变得难以察觉地小