how many 1/3inch cubes does it take to fill a box with width 2 and 2/3 inches, length 3 and 1/3 inches, height 2 and 1/3 inches.

Question

how many 1/3inch cubes does it take to fill a box with width 2 and 2/3 inches, length 3 and 1/3 inches, height 2 and 1/3 inches.

Answer 1

The volume of a 1/3 inch cube is 1/3 (1/3) ( 1/3) = 1/27 in³.

The volume of the box is V = lwh. Convert the mixed numbers to improper fractions.

V = (8/3)(10/3)(7/3) = 560/27 in^3.

How many 1/27 are contained in 560/27? That answer is determined by the operation of division.

(560/27) / (1/27) = 560

Another way to think about it.

(8/3) / ( 1/3) = 8 , so you can have 8 cubes along the width.

(10/3) / (1/3) = 10, so you can have 10 cubes along the length.

(7/3) / (1/3) = 7, so 7 cubes along the height

(8)(10)(7) = 560 cubes.