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Unfortunately, there is no officially sanctioned method for blocking just a portion of a page from the index. As others have mentioned, there are tricks that might do it, but their effectiveness is inconsistent, and most of them will run the risk that Google could treat it as a red flag of some sort. More often, the results just end up being unpredictable (especially with JavaScript) and end up causing additional grief for your developers and visitors. Most of the time, if you're dealing with substantial amounts of content you don't want indexed, I'd look for other solutions, such as grouping that content or making sure more of your content on any given page is unique. Unfortunately, that depends a lot on why you want it blocked, so it's hard to give a one-size-fits-all answer.