Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 7 Number Sense
Problem
Solution

1) Express 0.0000000056 ÷ 0.00000024 as a fraction in lowest terms.

 Best to use scientific notation here:

5.6x10-9 =      56x10-10 = 56⁄2400 = 7⁄300
2.4x10-7     2400x10-10
2) The fraction 11/14 is fairly close to 1. How many fractions are there between 11/14 and 1 that have a prime number denominator smaller than 14?
  1. The prime numbers less than 14 are 2,3,5,7,11 and 13
  2. 11/14 = .7857
  3. 4/5 = .8 so this works
  4. 6/7 = .857 so this works
  5. 9/11 and 10/11 work
  6. 11/13 and 12/13 work
  7. There are 6 fractions 4/5, 6/7 9/11, 10/11, 11/13 and 12/13

3) Joe mixes sodas to make the Joe Special. A Joe Special has 2 parts cola to 3 parts orange soda to 3 parts cream soda. If he's going to fill a 64 ounce bottle with his soda special, how many ounces of cola will he need?
  1. There are a total of 2 + 3 + 3 parts to Joe's recipe = 8 parts.
  2. He will need 2/8 x 64 = 64/4 = 16 ounces

Problem
Solution
4) The length of a picture is enlarged by 50% and the width is enlarged by 25% producing an odd looking picture. By what percent is the area enlarged? Express your answer to the nearest tenth of a percent. (Hint: you can choose any dimensions that are easy for you to work with.) Use L for the original picture's length and W for its width.
  1. The original picture's area is LW
  2. The enlarged picture's area is
    (1.5L x 1.25W)= 1.875 LW
  3. The enlargement is 1.875 LW / LW = 1.875 times the area of the original picture = an enlargement of .875 = 87.5%
5) Jerri has 63⁄4 yard of rope. He needs pieces that are 12⁄3 yards long to make belts for costumes. How many belts can he make? Convert to improper fractions, then to a common denominator and divide:
27⁄4 / 5⁄3 = 81⁄12 / 20⁄12 = 81/20 = 4 belts