Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 7 Number Sense
Problem
1) Jimmy is 10/9 as tall as Ying'ai. Ishmael is 4/5 as tall as Amanda. The difference between Amanda and Ying'ai is 4 inches. Ishmael is 14 inches shorter than Ying'ai. Ying'ai is 4 feet 6 inches tall. How tall is Jimmy?

2) A two digit number is divided by a two digit number with quotient a one digit number. The five digits used are 1, 2, 4, 7, 8 and each is used only once. What is the larger two digit number?

Problem
3) Donna has 1/8 tank of gas remaining when she pulls into a gas station. After she puts 15 gallons of gas in her car, the gas gauge reads 3/4 full. How many gallons does Donna's tank hold?

4) One tactic for adding fractions with complicated denominators is to use their prime factorizations to find a least common multiple. Try that here: What is the denominator for the sum
    a     +     b  
  924       364
when expressed as a single fraction in lowest terms?

5) What is the smallest whole number n so that