Consider R to hold the value 250 ohms. Now you have been told to calculate "R+150". Will the result be 400 ohms or "250 ohms + 150" as R has a unit whereas 150 does not?
P.S. I know its a stupid question but if someone could clarify, I'd be eternally grateful!
On
Physical quantities and "common" numbers behave quite differently, because of the way they're defined.
Every physical value is written like $nu$, where $n$ is a real number and $u$ is a unit. The problem arises when you want to manipulate the unit part $u$ with some other (incompatible) unit (including a dimensionless unit). You can think that every unit $u$ belongs to some set $S_d$ that possess every other unit with the same physical dimension $d$ (where physical dimensions are values like length, time, energy, ..., and every product of them).
For example
$S_{\text{distance}} = \left\{\text{m},\text{cm},\text{inch},\text{AU},... \right\}$
Of course every non-null set $S_d$ has infinite elements, as every unit $u$ can be multiplied by some real number $a \in \mathbb{R}$, creating a new different unit $au$ that also belongs to $S_d$. More strongly, selecting a fixed $u_0 \in S_d$, every other unit $u \in S_d$ can be written as $a u_0$ for some $a \in \mathbb{R}$ (think of how we convert units of a same dimension, it's just multiplying by a real number, like $\text{m} = 10^3~\text{mm}$).
This way we can define sum of units:
$u_0 + u = u_0 + au_0 = (1+a) \, u_0$
So summing two different units from a same dimension has no problem whatsoever. For example, $1~\text{m} + 1~\text{cm} = 1.01~\text{m}$.
Another thing we can define is the product of units. This is when things get interesting, because if we multiply two not-dimensionless units (that does not have to be the same dimension) we always have a unit from a different dimension. That is, if $u \in S_d$ and $u' \in S_{d'}$, then $uu' \in S_{dd'}$. That is how we define non-base dimensions (like resistance). For example
$\text{resistance} = \text{mass} \cdot \text{length}^2 \cdot \text{time}^{-3} \cdot \text{current}^{-2}$
(is worthy noting that the base dimensions are as arbitrary as any other dimensions, they're just defined like that by convenience, but there is a finite number of base dimensions as we know)
Also, we have an multiplicative identity, that is the dimensionless unit $1$.
In some way, those $S_d$ sets behave very like $R^n$ spaces, as we have an multiplication (in the case of real spaces, it's the Cartesian product) that operates between sets and a sum that operates inside a set, although we didn't defined very well negative or null units. That defines a mathematical ring or even a field if I'm not mistaken.
With all that, we can make a rigorous definition of physical units, but for answering you question, note that we never sum units of different dimensions. That is like summing an vector to a scalar: If it's not defined, it just not works. We can think in a lot of ways of making it work, but it will be a brand new definition that does not correspond to the physical reality. So 250 ohm + 150 is as meaningless as $(1,2,3) + 4$.
"250 ohms + 150" is meaningless if we assume that 150 is a pure number. The addition will only be meaningful if the two quantities have the same units of measurement, in this case, if "150" represents a quantity that is a resistance. I think you can safely assume that "150 ohms" is what was meant.