I have installed both the free word app
The original free word app didn't support editing. Microsoft recently announce the free app would support limited editing. You need office 365 to do full editing.
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Free apps
Apple iWork
iWork by Apple -- free with newly purchased iPads
http://www.imore.com/how-get-all-iwork-apps-iphoto-and-imovie-free-eligible-ipho ne-or-ipad
iWork for iCloud Beta
https://www.apple.com/iwork-for-icloud/
Citrix ShareFile QuickEdit
"Is the simplest document-editing tool available for iOS devices. Open, view, create and edit Microsoft® Word, Excel® and PowerPoint® files — right from your iPod®, iPhone® or iPad®!" Was Office² HD.
https://itunes.apple.com/gb/app/id364361728?mt=8
Kingsoft Office
"Read, edit PowerPoint files, and read Word documents on your iPhone or iPad, Share it by cloud storage."
http://www.kingsoftstore.com/office-free-ios
Quickoffice
Quickoffice is an application available for iOS and Android tablets and phones that lets you view, create, and edit Microsoft Office, as well as view and annotate PDF files. Connect Google Drive to Quickoffice for cloud storage so that you can easily access and edit files from your tablet, phone, or computer and know that your files are always up-to-date
https://support.google.com/quickoffice/answer/2986862?hl=en&ref_topic=2986859
CloudOn
Client front end to a Microsoft Office running on a server
"CloudOn brings Microsoft Office® to your iPhone & iPad and links it to your Box, Dropbox, Google Drive and SkyDrive accounts." Free for a give number of documents.
https://itunes.apple.com/us/app/cloudon/id474025452?mt=8