# Solutions

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**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 ÷ 4^{1}/_{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.