Series is a queue: one path, so every ohm stacks — $R_t = R_1 + R_2$, and the total always lands ABOVE either resistor. Parallel is extra doors: every new branch makes the flow easier, so the total drops BELOW even the smallest branch — always. The relation is product over sum: $R_t = \dfrac{R_1 R_2}{R_1 + R_2}$ (read aloud: R-total equals R-one R-two over R-one plus R-two).

Two nuggets worth owning: two EQUAL branches halve — $R/2$, no arithmetic — and the instinct check comes free before any computing: series above both, parallel below both. An answer on the wrong side of that line is wrong before the units even get a word in.