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:
  1. Convert both numbers to scientific notation:


  2. Modify the larger number's exponent until it matches the lower one's exponent:


  3. Divide the 2, noticing that the exponents cancel, and reduce =


    _______________
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. Convert 11/14 to a decimal = _________

  3. Starting with each denominator (let's call it n), compute the decimal representation of (n-1)/n, (n-2)/n, until the decimal falls below the above value.
  4. Do this for each prime denominator:



    =
  5. There are _______ fractions between 11/14 and 1

Problem
Solution

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 _____ parts to Joe's recipe.

  2. The fraction of 64 ounces that 2 of these parts are is ______

  3. He will need ____ x 64 = _____ ounces.
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 _________

  3. Divide these 2 and convert to percent to get the size increase: ____________

  4. Subtract 100% to get the enlargement factor = ______________
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:



= _____ belts
Note: You could also do it with decimals.