Question

To make four and a half gallons of ice cream it takes 6 3/10 gallons of milk how many gallons of milk does it take to make one gallon of ice cream

Answer 1

Ice cream = 4 1/2 gallons
milk = 6 3/10 gallons

ice cream: 4 1/2 = (4*2 + 1)/2 = 9/2
milk: 6 3/10 = (6*10 +3)/10 = 63/10

milk:ice cream  proportion: a:b = c:d  where a*d = b*c
a = 63/10 ; b = 9/2 ; c = x ; d = 1

63/10:9/2 = x:1
63/10 * 1 = 9/2 * x
63/10 = 9x/2
63/10 * 2 = 9x/2 * 2
126/10 = 9x
126/10 * 10 = 9x * 10
126 = 90x
126/90 = 90x/90
1 36/90 = x

x = 1 36/90  simplified to 1 13/30

1 13/30 gallons of milk will make 1 gallon of ice cream.