When you take a whole item and break it into equal parts, what you get is one — or more — of those equal parts; these are known as fractions. This may sound very math-y and complicated, but each of us works with fractions all the time and may not even realize it! Slicing up pizza for a group of friends, estimating the amount of gas in the gas tank, and calculating the number of hours slept (or not slept!) are just a few instances when we likely work with fractions.
This week’s word problems give your child an opportunity to practice fractional reasoning. So take a look below and choose the problem that’s the right skill level. Have them give it a try. And when they feel they’ve found the answer, check their solution against ours.
Lower Elementary:
Question: Derek has won 3 awards. Hansel has won 1 award. What fraction of all the awards did Derek win?
Upper Elementary:
Question: Gasoline costs $1.45 per litre. If a car’s gas tank holds 15 litres in total and is only 1/5 full right now, then how much will it cost to fill up the tank?
Middle School:
Question: An ant is 1/16 of an inch tall. A middle school student is 41/2 feet tall. The student goes to a learning centre that is 54 feet tall. If we scale by height, then how tall would a learning centre for ants be?
High School and Up:
Question: A man throws a computer off of a platform straight to the ground. It falls 16 feet and hits the ground in 1/2 of a second. Consider this equation for vertical distance traveled in terms of initial velocity, time, and acceleration due to gravity (32 feet/second2):
(distance) = (initial velocity)(time) – 1/2(acceleration due to gravity)(time)2
What is the initial velocity of the computer?
(Hint: The computer is traveling straight down, so the distance it travels is -16 feet in this instance.)
Solutions
Excellent! Are you ready to check your child’s answer? Look below to see if their solution matches ours.
Lower Elementary:
Answer: 3/4
Solution: To find the fraction, we first need to add up all of the awards to find the whole: 3 + 1 = 4. Derek won 3 out of the 4 awards, so the fraction of all the awards that Derek won is 3/4.
Upper Elementary:
Answer: $17.40
Solution: If the gas tank is 1/5 full, then it will need 4/5 × 15 = 12 litres of gas to fill it. The 12 litres of gas it takes to fill the tank costs $1.45 × 12 = $17.40.
Middle School:
Answer: 3/4 of an inch
Solution: The learning centre is 54 ÷ 41/2 = 12 times the height of the student. So, the learning centre for ants should be 12 times the height of the ant. Since 1/16 × 12 = 12/16 and 12/16 reduces to 3/4, the learning centre for ants would be 3/4 of an inch tall.
High School and Up:
Answer: 24 feet per second straight down
Solution: If we plug all our given values into the equation, we get this:
-16 = x(1/2) – 1/2(32)( 1/2)2
If we simplify that equation, we get this:
-16 = x(1/2) – 4
If we then solve for x, we get -24. The initial velocity of the computer is therefore 24 feet per second straight down.
Mathnasium meets your child where they are and helps them with the customized program they need, for any level of mathematics.
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