A large resistor in series (parallel) with a small resistor has the resistance of the larger (smaller) one, roughly?
The authors have confused things by combining the series and parallel situations in one sentence.  I would re-write it as follows:
&quot;A large resistor in series with a small resistor has the resistance of the larger  one, roughly. So you can “trim” the value of a resistor up connecting a second resistor in series: to trim up, choose an available resistor value below the target value, then add a (much smaller) series resistor to make up the difference.&quot;
For the series case, the equivalent resistance of two resistors in series will be the sum of the two resistor values.  If you want a 110 Ohm resistor, you could use a 100 Ohm and a 10 Ohm resistor in series.
&quot;A large resistor in parallel with a small resistor has the resistance of the  smaller one, roughly. So you can “trim” the value of a resistor down by connecting a second resistor in parallel: to trim down, choose an available resistor value above the target value, then connect a (much larger) resistor in parallel.&quot;
For the parallel case, remember that the equivalent resistance of two resistors in parallel will be less than the resistance of the lower value resistor.