Which of the following is the HIGHER gear ratio.

46/18 or 44/16?

Just do the math - 46/18 = 2.55, 44/16 = 2.75. For gear inches multiply by ~27" 1st = ~69", 2nd = ~74".

I didnt know how to compute the figures. So the 44/16 is the higher ratio correct??

What i am trying to do is decrease the amount of pedal revoultions to go the same speed

Is it worth the trouble to change sprockets seeing as how the figures are quite close?

Just get a larger cog.

no I think he wants a smaller cog.

I assume you realize the force required will go up in direct proportion to how much the pedal revolutions go down.

I think you're right.

Yes i know it will be slightly harder to pedal but thats ok. I have a 20in. bike geared 34/20 and you will pedel your butt off and not be going past walking speed. Im not a teenager anymore.

20" wheels?
or frame size?

that is a higher gear ratio
bigger chain ring turning your [probably a Fixie] smaller cog more often ..

people who race on a velodrome, bring a box full of chainrings and cogs
to the track, because, to them, it does matter ..

20in. muscle bike. Just for cruising but we have some light hills in our area.

Divide the front chainring by the rear cog. Bigger result = bigger gear.

Bigger charinring = smaller cog (rear) = go more distance per pedal revolution = go faster = more force on the pedals.
Smaller chainring = bigger cog (rear) = go less distance per pedal revolution = go slower = less force on the pedals.

But that's not all you asked. Is that difference significant? Not really. Those ratios are comparable to about 51 and 55 gear-inches on a bike with the more common 700c wheels. That difference is about "one click's worth" on a modern zillion-speed indexed system. You can feel the difference if you are trying to maintain an optimum cadence riding for speed, but otherwise it won't matter one bit. If you are changing your gearing because you are changing your riding style, then you need to reconsider.