George is making 8 gallons of Tropical punch. He has already poured in 1 3/4 gallons of pineapple juice and 2 1/2 gallons of orange juice. The only other ingredient is 7-Up. How much 7-Up does George need in gallons?

1 Answer
May 5, 2018

Answer:

George will have to add #3 3/4# gallons of 7-Up to bring the total to #8# gallons.

Explanation:

Add the gallons of juice that he has already used. Subtract that from #8# gallons.

#1 3/4 + 2 1/2#

Convert both mixed fractions to improper fractions. Multiply the denominator by the whole number, add the numerator, and place the result over the denominator.

#((4xx1+3))/4 + ((2xx2+1))/2#

Simplify.

#7/4 + 5/2#

When adding or subtracting fractions, they must have the same denominator. Multiply #5/2# by #2/2# to get an equivalent fraction with #4# as the denominator.

#7/4+5/2xx2/2#

Simplify.

#7/4+10/4#

#17/4#

George has already poured in #17/4# gallons of juice.

To determine how much 7-Up he needs to add, subtract #17/4# gallons from #8# gallons.

#8-17/4#

Any whole number is understood to have a denominator of #1#. #(n=n/1)#

Rewrite the expression.

#8/1-17/4#

Multiply #8/1# by #4/4# to get an equivalent fraction with #4# as the denominator.

#8/1xx4/4-17/4#

Simplify.

#32/4-17/4#

#15/4#

Convert #15/4# to a mixed number. Divide #15# by #4# to get a whole number quotient and a remainder. The whole number quotient is the whole number of the mixed number, the remainder is the numerator, and the divisor #(4)#, is the denominator.

#15-:4##=##3# #"R"# #3#

#15-:4=3 3/4#

George will have to add #3 3/4# gallons of 7-Up.