MHB Understanding Unit Cancellation in Physics Equations

[copperfox]

here's the question:

a = b/e
b = 1 kg m^-1
e = 1 kg m^-2

what is a? including units

I assume it's to do with cancelling out the units when you divide but I really don't know what the answer is

 

[I like Serena]

here's the question:

a = b/e
b = 1 kg m^-1
e = 1 kg m^-2

what is a? including units

I assume it's to do with cancelling out the units when you divide but I really don't know what the answer is

Hi copperfox! Welcome to MHB! ;)

Indeed. It's about canceling out the units.
It works like this:
$$a=\frac be
= \frac{1\cdot\text{kg}\cdot\text{m}^{-1}}{1\cdot\text{kg}\cdot\text{m}^{-2}}
= \frac{1\cdot\cancel{\text{kg}}\cdot\text{m}^{-1}}{1\cdot\cancel{\text{kg}}\cdot\text{m}^{-2}} \cdot\frac{\text{m}^2}{\text{m}^2}
= \frac{1\cdot\text{m}^{1}}{1\cdot\text{m}^{0}}
= \frac{1\cdot\text{m}}{1\cdot1}
= 1\,\text{m}
$$

 

[HOI]

Equivalently, $\frac{b}{e}= \frac{1\frac{kg}{m}}{1\frac{kg}{m^2}}= 1\frac{kg}{m}\frac{m^2}{kg}= 1\frac{kg}{kg}\frac{m^2}{m}= 1 m$