Solve for Remaining Water: 1/12 Hourly Reduction Over 4 Hours

Question

A full bottle of water has a small hole in it. Every hour the amount of water in the bottle decreases by112 \frac{1}{12} .

How much water remains in the bottle after 4 hours?

Video Solution

Solution Steps

00:00 Found the remaining part in the bottle after 4 hours
00:03 Given the amount that decreased after 4 hours
00:05 Therefore, subtract the given amount from the whole
00:10 Convert the whole to the appropriate fraction
00:16 Subtract in the common denominator
00:20 Calculate the numerator
00:24 Reduce the fraction as much as possible
00:27 Make sure to divide both numerator and denominator
00:34 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll subtract 112\frac{1}{12} from the full bottle (represented as '1' or 1212\frac{12}{12}) for each hour for a total of 4 hours:

  • Initially, the bottle is full: 1212\frac{12}{12}.
  • After 1 hour, subtract 112\frac{1}{12}:
    1212−112=1112\frac{12}{12} - \frac{1}{12} = \frac{11}{12}.
  • After 2 hours, subtract another 112\frac{1}{12}:
    1112−112=1012=56\frac{11}{12} - \frac{1}{12} = \frac{10}{12} = \frac{5}{6} after reduction.
  • After 3 hours, subtract another 112\frac{1}{12}:
    56−112=1012−112=912=34\frac{5}{6} - \frac{1}{12} = \frac{10}{12} - \frac{1}{12} = \frac{9}{12} = \frac{3}{4} after reduction.
  • After 4 hours, subtract another 112\frac{1}{12}:
    34−112=912−112=812=23\frac{3}{4} - \frac{1}{12} = \frac{9}{12} - \frac{1}{12} = \frac{8}{12} = \frac{2}{3} after reduction.

Therefore, the amount of water that remains in the bottle after 4 hours is 23\frac{2}{3}.

Answer

23 \frac{2}{3}

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Subtraction of Fractions

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