The melakha of Building refers to putting up buildings as well as fixing certain items. The prohibition includes minor improvements, such as installing a door or window, pounding a nail into a wall, gluing a hook onto a wall, or sealing up a small hole in a wall. One may not tighten the screws on the handle of a door or closet, insert a broom handle into the broom shaft, or assemble a bed or table with nails, screws, or glue. Reattaching a chair leg or table leg is forbidden as well.
A baby carriage or stroller, a folding table, a folding chair, a cot, and a playpen may be opened on Shabbat, because their parts are already connected before Shabbat, and they are designed to be easily opened and closed. However, if opening an item requires screwing or unscrewing, this is forbidden, as it involves forging a strong and permanent connection. One may add or subtract leaves from an extendable table, as long as this can be done easily and does not involve strong connections.
The melakha of Cutting is defined as cutting stone, metal, boards, and the like to the proper size to use them to put up a building or fix an item. It does not apply to food. For example, one may cut cake (and other foods) and peel oranges (and other fruits). One may also open cans of food and bottles of wine on Shabbat.