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:**

*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 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***) – 1/2(**

*time***)(**

*acceleration due to gravity***)2**

*time*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.