Amy has a bucket which contains 4 2/3 gallons of water. She pours out 1/4 of the water. After several hours pass, 3/7 of the water remaining in the bucket evaporates. How many gallons of water remain?
Give your answer as a fraction. ____ gallons
Here's How to Crack It
Your impulse may be to convert all those fractions into decimals. Don't. First off, they're fairly messy as decimals (3.7 ~ 0.42857 ... ), and secondly, there are some nice simplifications we can do with the fractions.
Start with that 4 2/3 gallons. Convert it into an improper fraction, which means it is 12/3 + 2/3 = 14/3. Now we want to find 1/4 of 14/3, and then 3/7 of that. So we want to find 14/3 x 1/4 x 3/7.
Notice that we can simplify the 3 in the denominator of the first fraction with the 3 in the numerator of the last fraction, leaving us 14/1 x 1/4 x 1/7.
Simplify a 7 from the top of the first fraction and the bottom of the last, leaving 2/1 x 1/4 x 1/1.
Now simplify out a 2 from the first and middle fractions, leaving 1/1 x 1/2 x 1/1. Enter in 1 on the top of the fraction box, and 2 on the bottom.