12 Pieces of Chalk

by Gary Salisburger
(Kent, Washington)

Ming and Chuck were walking home one afternoon and decided to draw a chalk line on the road from school to Chuck's house.

They started out with a box of chalk and realized that one piece only lasted for two-thirds of a block.

If they had 12 pieces of chalk in the box, for how many blocks were they able to draw a line? How do you know?


Solution

1 piece ----------- 2/3 of a block

2 pieces ---------- 2/3 + 2/3 = 4/3 = 3/3 + 1/3 = 1 + 1/3

3 pieces ---------- 1 + 1/3 + 2/3 = 1 + (1 + 2) / 3 = 1 + 3/3 = 1 + 1 = 2

Based on this pattern, 6 pieces can do 4 blocks

Therefore, 12 pieces can do 8 blocks.

A quicker way to solve this problem is to multiply

12 by 2/3

12 times 2/3 = (12 * 2) / 3 = 24 / 8 = 8