# Sarah was cutting fabric for a quilt. She cut a strip of fabric that was 19 1/8 inches long into 5 equal pieces. When she was finished cutting, Sarah had a piece that was 2 1/4 ...

Sarah was cutting fabric for a quilt. She cut a strip of fabric that was 19 1/8 inches long into 5 equal pieces. When she was finished cutting, Sarah had a piece that was 2 1/4 inches long. How long was each piece that she cut for the quilt

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You need to subtract the length of `2 1/4` inches from the total length of `19 1/8` , such that:

`19 1/8 - 2 1/4 = 153/8 - 9/4`

You need to bring the fractions to a common denominator, such that:

`19 1/8 - 2 1/4 = (153 - 18)/8`

`19 1/8 - 2 1/4 = 135/8`

You need to divide the resulted length of `135/8 = 16 7/8` to 5 pieces, such that:

`(135/8)/5 = 135/40 = 27/8 = 24/8 + 3/8 = 3 3/8`

**Hence, evaluating the length of each piece yields `3 3/8` inches long.**

Sarah cut a strip of fabric that was 19 1/8 inches long into 5 equal pieces. Let the length of each of these pieces be represented by x. When she was finished cutting, Sarah had a piece that was 2 1/4 inches long.

The total length of fabric she started with was 19 1/8. This is also equal to 5*x + 2 1/4

Equating the two allows for x to be determined.

5x + 2 1/4 = 19 1/8

5x = 19 1/8 - 2 1/4

5x = (19*8 + 1 - 16 - 2)/8

5x = 135/8

x = 27/8

Each piece was cut to a length of 27/8 inches.