You should basically play the notes A (Right below middle C) C#, E and G with the 1st, 2nd 3rd and 5th fingers.
The meaning of a chord in the root position is that the key note of the chord (A in our case) is placed as the lowest note of the chord. The A7 chord is made out of a major third which defines it as a major chord, then two minor third on top of each other.
In order to be able to play all piano chords quickly you should first be familiar with the chords you absolutely, positively need to know. The greatest thing about this E-book is that it has very clear pictures that show the exact fingering.
Notice that in both cases the thumb will always be placed on the white notes - that's very convenient even for the unskilled hand. When playing four tone chords we still apply the rules we've learn in the three tone chords.
Every arpeggio in that group will have the same fingering, only it will start from a different note.

A commonly-used harmonic device is to shift the key center back and forth between pairs of closely-related major and minor keys. Special Note: Almost every music theory academician considers C major and A minor to be relative keys -- relative because they share the same key signature - no sharps or flats. Sight Reading tip: If you started in the key of C, but come upon the chromatic note G#, be alert.
Other Examples: Europa, Still Got the Blues, Windmills of Your Mind, Georgia, My Funny Valentine, God Bless the Child, countless Jazz standards and classical pieces! The above graphics are in high definition 600 DPI and will print brilliantly even if the screen display is not that good. When playing an F# major and Eb minor chord we'll apply the same fingering we use when playing a chord with only white keys. The fingering for a Bb minor chord will be 231-231-2 in the right hand and 321-321-3 in the left hand.
An example of such a closely-related key pairing is C major and A minor (see Special Note below).

G# is the leading tone Ti in the key of A, a very strong indicator that a modulation from C major to A minor may be occuring. However if you read this exercise from right to left you'll be playing the order of the descending scale. This harmonic device is used so extensively -- in classical, ragtime, pop, blues, rock, jazz -- that it is a very valuable skill to recognize it by sight in written music and by sound when you hear it. The harmonic tension of the dominant chords coupled witht the harmonic release of the tonic chords are strong enough to lead the ear to each new key center almost seamlessly. The reason: The V chord of A minor is E, which contains the leading tone G# (Ti), clearly not in the C major key siganature. Combine this sound recognition with your knowledge of the theory (notes, Roman numeral analysis, solfege) and you have made a huge addition to your ability to play by ear.

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