The piece of music that I am learning is 60 measures long. There are 13 beats in every measure, and every eighth note lasts for 1 beat. The last 17 measures of this piece are the finale. In every measure of the finale, there are 7 eighth notes played at middle C. If middle C never occurs in this piece outside of the finale, for what fraction of the whole piece do I play middle C

A fraction is a portion of a whole or, more broadly, any number of equal parts.
In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
A common, vulgar, or simple fraction consists of a numerator above a line and a non-zero denominator below (or after) that line.
Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.

To find for what fraction of the whole piece do you play middle C:

Since 7 out of every 13 beats in the finale are played at middle C, [tex]\frac{7}{13}[/tex] the finale is played at middle C.

The finale is 17 measures out of a 60-measure piece or [tex]\frac{17}{60}[/tex] of the whole piece.

[tex]\frac{7}{13}[/tex] of [tex]\frac{17}{60}[/tex] is [tex]\frac{7}{13}[/tex] x [tex]\frac{17}{60} = \frac{119}{780}[/tex]

Therefore, [tex]\frac{119}{780}[/tex] for a fraction of the whole piece you play middle C.

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