As some others mentioned there are a few things to consider here:
1) The distance between your subject and the camera is about the same as the distance between your subject and the background. Get closer to your subject and zoom in. The further the background is from the subject relative to the camera, the better chance you have of blurring the background..
2) The Depth of Field on point and shoot cameras is a lot bigger than on DSLRs due to the much smaller sensor size. Some point and shoots can have a 35mm equivalent of f65 for their apeture sizes. That makes for a huge depth of field diffference. When trying to blur the background with a point and shoot, you need to do more than just change the aperture. You need to get close and zoom in as that accentuates the differences in subject to camera distance vs. subject to background. Also, some people have had success shooting with the macro-mode on point and shoot cameras.
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