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I have many diagrams with different sizes. I try to reduce the size of each diagram.

Or:

I reduce the sizes of diagrams

Please tell me which one is correct and why?

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Both are possible. It depends on whether you want to suggest the action of 'reduce' is something you do once or many times. For example, you could say either:

One step in my review process before I finalise a document is I reduce the size of diagrams.

One of the steps in my review process before I finalise a document is I reduce the sizes of diagrams.

I apologise if that is confusing, but there is no definite answer to your question.

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Don't worry; native speakers have trouble with this one all the time. I know a song and the poor (native speaker) singer tries really hard to sing: "...When these kinds of questions..." but she just can't seem to remember and get over the natural tendency to say, "...these kind of questions..." which we hear every day..., and she gets so mixed up and sings it both ways throughout the song. Yes, it CAN sometimes be a little confusing, but I think you're already on the right track.

"This apple is red." (no problem) "These" apples are red. (Still with me?) "This is the kind I like!" (Still no problem?) "These kinds are different from the red ones"

If the "this" or "that" is singular, then so is the "kind", "sort", "type", "example", "variety" etc. If they are plural, so is the word they refer to:

"These types of boots bother my knees." "These examples of ostriches are almost never found."

The reason we get confused is because we're not completely sure what the subject is. If we know what the SUBJECT is, the VERB (and its number -plural or singular-) falls so easily into place, doesn't it?

"These kinds are wonderful!" (Subject="KINDS - ARE") Piece o' cake! "These kinds of tomatoes are wonderful!" (STILL "kinds are") Nothing has changed except we added this little adjective prepositional phrase: (of what?) "of tomatoes", but "KINDS" is still the subject, isn't it?

Now I suppose someone MIGHT try to say "These varieties of tomato..." or "These types of fish..." and I wouldn't necessarily "throw the book" at them, but how much better it sounds when everything agrees: "These types of fishes..." ("Fish" has an exceptional "es" plural when it includes different varieties.)

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