Question

Naya sells half the paintings in her collection and gives one-third of her paintings to friends, while she keeps the remaining paintings for herself. What fraction of her original collections does she keep?

Answer 1

`R = (1)/(6)`

Explanation:

Given that she sold half the paintings and gives out one-third

Required

Determine the fraction left with her

The relationship between the paintings is as follows;

Sold Paintings + Giveaway Paintings + Remaining Paintings = 1

From the question;

Sold Paintings = 1/2

Giveaway = 1/3

Represent Remaining Paintings with R

Substitute these values in the above formula

`(1)/(3) + (1)/(2) + R = 1`

Take LCM

`(2+3)/(6) + R = 1`

`(5)/(6) + R = 1`

Make R the subject of formula

`R = 1 - (5)/(6)`

Take LCM

`R = (6-5)/(6)`

`R = (1)/(6)`

Hence, the fraction of the paintings left with her is
`(1)/(6)`