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:
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 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:
Answer:  3/4 of an inch
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.

SEE HOW MATHNASIUM WORKS FOR YOUR SITUATION

Answer a few questions to see how it works

My Child is:

arrow
arrow

OUR METHOD WORKS

Mathnasium meets your child where they are and helps them with the customised program they need, for any level of mathematics.

HELP YOUR CHILD ACHIEVE THEIR FULL MATHS POTENTIAL

We have over 1,100 centres and we're expanding rapidly in the UK. Get started now.
  • Find a centre near you
  • Get a maths skills assessment for your child
  • Receive your child's customised learning plan
arrow
Get Started by Finding a Local Centre

Maths tutors near

Could not find Centre, try again