at the video store where you work the dvd cases are 5/8 of an inch wide. New shelf units are available that have 6 40-inch shelves. How many dvd should fit on a 6-shelf unit?

40/(5/8) =

40 * (8/5) = 320/5 = 64 dvds per shelf

64 * 6 = ________ total dvds

384

To determine how many DVDs can fit on a 6-shelf unit, we need to calculate the total width available on the shelves and divide it by the width of each DVD case.

First, let's calculate the total width of the shelves:
Total width = Number of shelves * Width per shelf
Total width = 6 shelves * 40 inches = 240 inches

Next, let's calculate the number of DVDs that can fit on the shelves:
Number of DVDs = Total width / Width of each DVD case
Number of DVDs = 240 inches / (5/8) inch

To divide by a fraction, we invert the divisor (5/8) and multiply:
Number of DVDs = 240 inches * (8/5) = 384 DVDs

Therefore, a 6-shelf unit can fit 384 DVDs.

To find out how many DVDs can fit on a 6-shelf unit, we need to calculate the total width of the shelves and then divide it by the width of one DVD case.

First, let's find the total width of the shelves:
Since there are 6 shelves and each shelf is 40 inches wide, we multiply 6 by 40:
6 shelves * 40 inches per shelf = 240 inches total width of the shelves.

Next, we need to determine how many DVD cases can fit in 1 inch of shelf space. We know that each DVD case is 5/8 of an inch wide. To calculate the number of DVD cases that can fit in 1 inch, we divide 1 inch by 5/8 inch:
1 inch / (5/8 inch) = 1 * (8/5) = 8/5 = 1.6 DVD cases.

Finally, we can find out how many DVD cases can fit on the 6-shelf unit by multiplying the total width of the shelves by the number of DVD cases that can fit in 1 inch:
240 inches * 1.6 DVD cases per inch = 384 DVD cases.

Therefore, a 6-shelf unit can fit approximately 384 DVDs.