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
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Learn how to derive the equation of an ellipse when the center of the ellipse is at the origin.