Welcome to the world of bipolar logic, specifically the 74S, 7400, and 74LS families.
Using a pulldown resistor generally won't work, and unused inputs MUST NOT be allowed to float. Rather, unused inputs must be tied either high or low. To tie an input low, ground it. To tie an input high, for the LS family use a 4.7k resistor to +5. Actually, anything between 1k and 10k will work. What you need to do is provide a current of 20 uA per input to pull it above 2 volts. Generally a single resistor can be used to pull up all the unused inputs on a chip.
Another way to do it is to use an unused inverting gate such as an LS00, LS02, LS04, etc. Tie the input low, and you can use the resulting high output.
Unused TTL inputs normally operate as if they are high. However, their input impedance is high, and they can show a remarkable sensitivity to pulses from all sorts of sources, and cause intermittent issues of a remarkable variety of symptoms. So make sure you tie ALL unused inputs of ALL chips either high or low. Keep in mind that tieing inputs low might seem the easiest approach, but you'll be pulling a nominal 400 uA per input, and this can add up quickly, causing both extra current capacity from you power supply and increased power dissipation.
Also note this applies in spades to 74HC series gates. Floating CMOS inputs are even more sensitive than bipolar. Fortunately, for 74HC ICs you can simply tie inputs to either +5 or ground.
I can't stress the need to tie ALL unused inputs to a fixed level. If you let inputs float, even for unused gates on a chip, you can get weird glitches in the sections you are using which will break your heart trying to debug. For beginners making small circuits this usually isn't a problem, but as you get to more complex circuits this can really bite you on the butt, and it will be intermittent and may depend on everything up to and including the phase of the moon. Develop good habits early and save yourself problems.
