Question

Jon has painted 4/5 of his house. The next day he painted 2/3 of what he had left. What fraction of the house is left to paint?

Answer 1

`\displaystyle(1)/(15)\text{ fraction of the house is left to paint.}`

Explanation:

We are given the following information in the question:

Amount of house painted by John =
`\displaystyle(4)/(5)`

House left to be painted =

`1-\displaystyle(4)/(5) = (1)/(2)`

The next day he painted 2/3 of what was left.

House painted next day =

`\displaystyle(1)/(5)* (2)/(3) = (2)/(15)`

Fraction of the house is left to paint =

`1 - \displaystyle(4)/(5)-(2)/(15) = (15-12-2)/(15) = (1)/(15)`

`\displaystyle(1)/(15)\text{ \bold{fraction of the house is left to paint.}}`

Answer 2

Jon has painted 4/5 of his house at the first day. Then

`1-(4)/(5) =(5)/(5) -(4)/(5) =(1)/(5)`

left.

The next day he painted 2/3 of what he had left. This is exactly 2/3 from 1/5. Mathematically you should multiply these two fractions:

`(2)/(3)\cdot (1)/(5) =(2\cdot 1)/(3\cdot 5) =(2)/(15)`

he has painted the second day.

Now count how much he has painted at first and second days:

`(4)/(5)+(2)/(15)=(4\cdot 3+2)/(15)=(14)/(15) .`

Then he has to paint

`1-(14)/(15) =(15)/(15)-(14)/(15)=(1)/(15) .`

Answer:
`(1)/(15) .`