Percents & Fractions
Congratulations to the Washington Capitals hockey team on winning the Stanley Cup! To celebrate the NHL champions, we have a few hockey themed problems for you to solve.
In the quest to win the Stanley Cup, the Washington Capitals played in four playoff rounds. During each round, they faced a different opponent in a best-of-seven series, in which the winner was the first team to win four games. What is the absolute difference between the greatest and least number of games that a team could play in four such rounds to become the Stanley Cup Champions?
On Sunday, May 13th, 224 of the nation’s smartest middle-school math minds will be in Washington, DC for the 2018 Raytheon MATHCOUNTS National Competition. The stakes are high, and the problems will be tough. Here are a few Sprint Round problems national competitors solved in 2017.
What is the maximum possible absolute difference between a two-digit integer and the two-digit integer resulting when the digits are reversed?
Sun City earned its name because it rarely rains there. In fact, it rains only 54 days each year there, on average. What percent of the days in 2018 is it expected to rain in Sun City? Express your answer to the nearest hundredth.
The percent of the days in 2018 it is expected to rain is 54/365 = 0.1479452055 ≈ 14.79%.
A baby rabbit moves 5 inches forward with each hop and his mother moves 14 inches forward with each hop. After the mother and baby each hop 10 hops in the same direction, the mother stops and waits for her baby to catch up. How many hops does the baby have to take to catch up?
This Wednesday (3/14) was Pi Day. Here are a few questions in honor of the day.
If Celia ate 1/4 of 2/3 of 1/2 of a pie, what fraction of the whole pie did she eat? Express your answer as a common fraction.
Celia ate (1/4)(2/3)(1/2) = 1/12 of the whole pie.
This month the 2018 MATHCOUNTS State Competitions will take place, so let’s look back at some of the 2017 State Sprint round problems and solve them in preparation.
Andre can complete 5/6 of a job in 3/4 of the time that it takes Michael to do the whole job. What is the ratio of the rate at which Andre works to the rate at which Michael works? Express your answer as a common fraction.
The snowfall in Mathopolis totaled 68.1 inches in 2015 and 11.2 inches in 2017. If the average yearly snowfall for 2015, 2016 and 2017 was 35.6 inches, how many total inches of snow fell in Mathopolis in 2016? Express your answer as a decimal to the nearest tenth.
Civil Rights leader and Nobel Prize winner Martin Luther King, Jr. was born January 15, 1929. On January 13, 1979 a 15-cent stamp was issued by the United States Postal Service as part of the Black Heritage Series of commemorative stamps. In 1979 it cost 15 cents to mail a first-class letter weighing up to 1 ounce, and the current cost to mail a first-class letter weighing no more than 1 ounce is 49 cents. Suppose $24,965,250 worth of the Black Heritage King stamps have been issued by the USPS.
Allie plans to make a fruit cake for her family plus four more to give away to friends. Shown here is a list of the ingredients required to make a fruit cake according to Allie’s recipe. How many ounces of mixed fruit are needed for Allie to make five fruit cakes, according to her recipe?
Each year Desmond and his family take part in the cultural celebration of Kwanzaa. The observance centers around the seven principles of Kwanzaa: Umoja, Kujichagulia, Ujima, Ujamaa, Nia, Kuumba and Imani. Suppose Desmond writes each of the five letters of the seventh principle, Imani (Swahili for Faith) on its own index card. If Desmond places the five cards in a bag and randomly chooses three cards, what is the probability that he chooses the three letters of the fifth principle, Nia (Swahili for Purpose)? Express your answer as a common fraction.