How many cubic blocks of side length 1/6 inch would take to fill a rectangular prism with a length, width, and height of 1/2 cm, 1/6 cm, and 1/2 cm respectively ?

9 blocks

Step-by-step:  

One way in which to do this problem is to find the volume of the rectangular prism and then divide that by the volume of one  cubic block of side length 1/6 inch.

V = (length)(width)(height) = (1/2 cm)(1/6 cm)(1/2 cm) = 1/24 cm³.

Volume of one cubic block of side length 1/6 cm is (1/6 cm)³ = 1/216 cm³.

Dividing 1/24 cm³ by 1/216 cm³ yields 216/24 blocks, or 9 blocks.

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative