Use an electric drill with a masonry bit to drill a diagonal series of small holes into the cracked tile, keeping drilled holes less than 1 inch (2. 54 cm) apart. Split the tile through the horizontal hole-line by using a ball-peen hammer to tap a cold chisel into the tile. Tap very lightly so as not to crack neighboring grout joints. Remove the loosened pieces. Use a flat bar to pry up any shards that you cannot get up by hand. Scrape the remaining old mortar from the subfloor using a stiff-bladed scraper. It is not important that you get every last bit up. Just make sure the area is fairly clean of mortar. Vacuum up any loose dirt or debris.
Mix your grout in a clean container with fresh water. Slowly add a little bit of water, mix and then repeat until you reach a consistency of pancake batter. Using a grout float, scoop out a bit of grout. Place the float at a 45-degree angle and in diagonal strokes spread the grout in the gaps between the tiles. After 20-30 minutes your grout should start to harden, and you can clean the surface of tiles with a wet sponge. You may need to do 2-3 rounds of cleaning.
