Question

Given that 1 joule = 1 newton × 1 meter and 1 volt = 1 joule per coulomb, show that the units

newtons/coulomb and volts/meter are equivalent.

Answer 1

You have two equations:
1st:
`1J=1N*1m`
and
2nd:
`1V=(1J)/(1C)`

from the second equation you can extract Joule:

`1J=1V*1C`
you compare right side of the equation above to the right side of the 1s equation:

`1V*1C=1N*1m`

then you devide both sides by 1C and by 1m and you get:

`(1V)/(1m)=(1N)/(1C)`