If you give a bottle of breastmilk and baby only drinks some of it, do u have to throw out the remainder even if u put it in fridge right after?

For me, I will keep it in the fridge immediately and offer it for the next feed. If it still doesn't finish, then I will use it for milk bath. Breast milk is too precious to me as I have limited supply. Haha. Always do the smell and taste check before offering the milk to baby. So far so good, have been doing so since she was about 3 months old. No mishaps!