During the day Bob drank #1/6# of a gallon of water, #1/8# gallon of water and #5/12# gallon of water. How much water did Bob drink altogether?

1 Answer
Oct 16, 2017

See a solution process below:

Explanation:

To add or subtract fractions they must be over a common denominator:

First, find the common denominator of each fraction by finding the least common multiple of the three denominators:

Multiples of #6 = 6, 12, 18, color(red)(24), 30...#

Multiples of #8 = 8, 16, color(red)(24), 32, 40...#

Multiples of #12 = 12, color(red)(24), 36, 48, 60...#

The Least Common Multiple is #color(red)(24)#

Now, we need to multiply each fraction by the appropriate form of #1# to make it's denominator #color(red)(24)# while not changing the value of the fraction:

#1/6 = 4/4 xx 1/6 = (4 xx 1)/(4 xx 6) = 4/24#

#1/8 = 3/3 xx 1/8 = (3 xx 1)/(3 xx 8) = 3/24#

#5/12 = 2/2 xx 5/12 = (2 xx 5)/(2 xx 12) = 10/24#

We can now add the three fractions:

#4/24 + 3/24 + 10/24 = (4 + 3 + 10)/24 = 17/24#

Altogether Bob drank #17/24# gallon of water.