Make sure the fireplace is completely cool before working. Put on safety goggles, a respirator mask and work gloves for protection.
Strike the broken flue tile in several places with the flue hammer. Use a flashlight to help you see while you work.
Pick out all the tile pieces and set them aside for later disposal.
Combine the cement masonry mortar with water, as directed by the manufacturer, in the 5-gallon bucket. Stir well using the scrap wood.
Lay a 1-inch-thick layer of the mortar over the replacement tile area inside the chimney using the trowel.
Set the new flue tile into the area, tapping lightly with the masonry hammer to ensure good contact between the mortar and tile.
Allow the mortar to set overnight before using your fireplace.