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Using archival-grade material will protect your photo from chemicals that could potentially damage it over time. Buy this mounting board at your local craft or frame store. The mount board will sit against the back of the picture frame. It helps protect the photo and keep it in place so it doesn't get warped over time. The "mount board" is the same thing as "foam core," and you'll see these terms used interchangeably on different products. Just like you did with the mat board, you'll need to cut the mount board down to size so it'll fit snuggly in the picture frame. Use your metal ruler and X-ACTO knife to make your cuts. It's really important that the mount board can't move around in the frame, so take the time to measure and carefully cut. If it is loose, the picture will get off-center and not look right in the frame. You can buy these at your local craft store. Position the picture in the middle of the mat board. Slip a photo corner over each corner of the picture, remove the adhesive, and press the corner down onto the mat board. Photo corners make it really easy to remove and switch out the picture in the future. There's no adhesive attached to the back of the actual picture, so there is no chance that it could get damaged. If you decide to just sandwich the picture between the mat board and the mount board, that is called a "floating mount." If you do this, make sure there is a firm fit in the frame so that the picture doesn't come loose and fall down. Look for an archival-grade adhesive tape. Most of these come in an easy-to-use dispenser, and you can use it much like you would packing tape. Line the edges of the mat board on each side with the adhesive. You can also use: linen hinging tape, press-on mounting tabs, or archival-grade double-sided tape. Be very careful to get the edges of the mat lined up perfectly with the edges of the mount board. Once it's in position, firmly run your hands along the edges to secure the 2 pieces together. Position the matted picture so that the picture itself is facing the glass part of the frame. Put the back of the frame in place and secure it down with the available tabs. Hang or display your new framed picture and enjoy your handiwork! If you're hanging the picture on the wall, make sure to use a level so that it's perfectly straight.

Summary:
Use an archival foam core for the mount board. Cut the mount board to fit inside the frame of your choice. Attach the picture to the mount board with photo corners. Apply a transfer adhesive to the edges of the back of the mat. Line up the edges of the mat to the mount board and press down firmly. Insert the matted picture into the frame and hang up the picture.