Question

Judy helped her mother make four sevenths litres of lemonade to treat their guests. She poured the lemonade into cups. Each cup had a capacity of one fifth litres. She filled some cups completely except for 1 cup. How much lemonade was in the cup that was not completely filled? Express fraction in simplest form

Answer 1

Through trial and error, if Judy fills 2 cups each 1/5 of a liter, then that's 2/5 of a liter so far.

Subtract this from the amount of lemonade.

4/7 - 2/5 = (4/7)*(5/5) - (2/5)*(7/7)

4/7 - 2/5 = 20/35 - 14/35

4/7 - 2/5 = (20 - 14)/35

4/7 - 2/5 = 6/35

There would be 6/35 of a liter left

1/5 = (1/5)*(7/7) = 7/35

Since 6 < 7, this means 6/35 < 7/35; in other words 6/35 < 1/5

It shows that the remaining 6/35 of a liter left over isn't enough to fill up a complete 3rd cup.

Answer: 6/35 of a liter