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As the number of iterations approaches infinity, the sum approaches 1.

Q: Why does one half plus one quarter plus one sixteenth and so on equal 1?

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1/2 + 1/4 + 1/8 + 1/16 = 15/16 or fifteen sixteenths. Expressed as a decimal, this is equal to 0.9375.

One of anything plus five of the same thing is equal to six of them.

One half.

5.25, or 5 and 1 quarter (5 1/4)

A quarter plus a quarter is a half. In U.S. coins, two quarters equals 50 cents.

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1/2 + 1/4 + 1/8 + 1/16 = 15/16 or fifteen sixteenths. Expressed as a decimal, this is equal to 0.9375.

1/4 + 1/16 = 5/16

In music, two quarter notes tied together get the same amount of beats as a half note: two beats. If one quarter note is one beat, and you put together two, you get two beats. Remember, one sixteenth plus one sixteenth equals one eighth. One eighth plus one eighth equals one quarter. One quarter plus one quarter equals one half. One half plus one half equals a whole. The same goes for rests, and later on you will probably get some thirty-second notes or sixty-fourth notes. You just go the opposite direction: two sixty-fourth notes equal a thirty-second note. Two thirty-second notes equal a sixteenth note. And then you go to eighths, quarters, halves, and wholes. I hope this helps!

Those two notes equal a dotted eighth note. In terms of beats, (assuming common time) then the eighth note gets a half a beat and the sixteenth note gets a quarter of a beat, so the two of them together get 3/4 of a beat.

One of anything plus five of the same thing is equal to six of them.

One half.

Those two notes equal a dotted eighth note. In terms of beats, (assuming common time) then the eighth note gets a half a beat and the sixteenth note gets a quarter of a beat, so the two of them together get 3/4 of a beat.

5.25, or 5 and 1 quarter (5 1/4)

A quarter plus a quarter is a half. In U.S. coins, two quarters equals 50 cents.

Four quarter notes is equal to one whole note (the empty note head with no stem). One whole note is held for four beats. Four quarter noes is also equal to two half notes (the empty note head with a stem). Each half note is equal to two quarter notes. To put it another way: one half note is worth twice the value of a quarter note. Four quarter notes is also equal to eight eighth notes (the filled note heads with flags). Each eighth note is worth half of the value of one quarter note. Four quarter notes is also equal to sixteen sixteenth notes (filled note heads with two flags). Each sixteenth note is worth half of the value of the eighth note or one fourth of one quarter note. Those are the most common divisions of four quarter notes. You can also mix and match those divisions; for example, four quarter notes takes up the same amount of time as one half note plus one quarter note plus two eighth notes. There are hundreds of thousands of configurations that could rewrite the value of those four quarter notes, which is just one reason why there is so much variation in the types of music it is possible to write!

15/16

Yes, half a cup (1/2) plus one quarter cup (1/4) is equal to three quarters cup (3/4) when added together.