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Lollipop - multiple Google accounts, setting the default

I have two Google accounts - one personal, one for work. I added the work account last, and it seems to show up as the default for the OS and apps I install. I'd like the personal account, which I added first, to be the default Google account for he device.

Can I change this without having to remove both accounts and add them again in the opposite order?

Edit: to clarify -- while each app will ask which account I want to use, that isn't what I'm asking about. I'm asking if we can change which account the device assumes is primary, and therefor which account it displays first. One would think the first Google account added to the device would be the default, but instead it seems to use the last instead.