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Word Problem Wednesday: Fractional Reasoning

Dec 16, 2020

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 on the next page.

Questions

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 gallon. If a car’s gas tank holds 15 gallons in total and is only 1/5 full right now, then how much will it cost to fill up the tank?

Middle School:
QuestionAn ant is 1/16 of an inch tall. A middle school student is 41/2 feet tall. The student goes to a learning center that is 54 feet tall. If we scale by height, then how tall would a learning center for ants be?

Algebra 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:
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:
Solution: If the gas tank is 1/5 full, then it will need 4/5 × 15 = 12 gallons of gas to fill it. The 12 gallons of gas it takes to fill the tank costs \$1.45 × 12 = \$17.40.

Middle School:
Solution: The learning center is 54 ÷ 41/2 = 12 times the height of the student. So, the learning center 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 center for ants would be 3/4 of an inch tall.

Algebra 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.

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