Darion needs 20 pieces of string 3/8 inch in length .He cut a 4 7/8 inch piece of string into pieces that are 3/8 of a inch long each. How many more pieces of string does he need?

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15 1/8

15

To determine how many more pieces of string Darion needs, we first need to find out how many pieces of string he has already cut from the 4 7/8 inch piece of string.

To calculate this, we need to divide the total length of the string piece by the length of each individual piece.

The length of the string piece is 4 7/8 inch, and each piece is 3/8 inch long.

To divide these fractions, we can convert them to a common denominator (in this case, 8) and then divide the numerator (the number on top):

4 7/8 ÷ 3/8

First, convert the whole number (4) to a fraction by multiplying it by the denominator of the fraction (8):
4 x 8 = 32

So, we have: 32/8 + 7/8 ÷ 3/8

Now, we can add the fractions:
32/8 + 7/8 = (32 + 7)/8 = 39/8

Finally, divide the combined fraction by the fraction representing the length of each piece:
39/8 ÷ 3/8

When we divide fractions, we multiply the first fraction (dividend) by the reciprocal of the second fraction (divisor). The reciprocal of 3/8 is 8/3:

(39/8) x (8/3) = (39 x 8)/(8 x 3) = 312/24

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 8:
312/24 ÷ 8/8 = (312 ÷ 8)/(24 ÷ 8) = 39/3 = 13

So, Darion has already cut 13 pieces of string.

Since he needs a total of 20 pieces, we subtract the number of pieces he already has from the total:

20 - 13 = 7

Therefore, Darion needs 7 more pieces of string.