Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 7 Number Sense
Problem
1) In the diagram the sum 1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 represents the area of the shaded sections. If the area of the entire rectangle is 1, what is the sum of the areas of the two unshaded regions?

2) For a baseball team, the ratio of the team's wins to its losses is 3:2. If the team continues at this pace, how many games will it win out of 110 games?
3) In the sequence below, what is the value of the 20th term?
  1   1
2 1 - 2
3 1 - 2 + 3
4 1 - 2 + 3 - 4

Problem
4) Mr. Tenpercent always marks up his retail price by 10% and then offers a 10% discount when he has trouble selling an item. If retail price for a particular item is $1000.00 what's his final price when he applies the discount?

5) Insert one additional set of parentheses to make the following number sentence true.
8 - 6 - 3 x (4 - 10) ÷ 2 + 1 = 18