Not drinking all of their tea?

I noticed that when I give my Japanese guests some tea, hot or cold, they never finish what I give them. There's always like 1/4 of the cup left behind. Plus they're really slow drinkers.

Is there a cultural reason for this? Maybe leaving some in the cup so I don't offer them any more?

I thought tea was supposed to be drunk slowly. But as far as I know, it is polite to drink until the very last drop in the cup.

Maybe leaving some in the cup so I don't offer them any more?

Maybe, especially if you're pouring new tea over the old without asking. But generally speaking, guests take their last sip as they stand up to go.

My husband is Japanese but raised in Hawaii however, my MIL leaves a little at the bottom b/c of the green tea leaves. I never drink the last sip b/c I dont want the brown rosted rice and green tea leaves to get stuck in my teeth ^_^

You should use a little sieve or a tea ball.

I noticed the slowness with one Japanese friend. ^.^ At the point where it became cold. I think people in the UK in general wouldn't want their tea to get cold, that's why they drink it more quickly probably... ?_?

I'm Japanese girl and high school student.

I think they wanted you to think that they were enjoying talking and they weren�ft hurry.
If you drink all cup tea soon, Japanese think �g he may be thirsty now and he may want more tea�h or �g he may be hurry now�h.
Japanese people tend to spend slowly time with their friend. So, they mean �g we were enjoyed tea with relaxing.�h