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

Answer:

$R = \frac{1}{6}$

Step-by-step 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

$\frac{1}{3} + \frac{1}{2} + R = 1$

Take LCM

$\frac{2+3}{6} + R = 1$

$\frac{5}{6} + R = 1$

Make R the subject of formula

$R = 1 - \frac{5}{6}$

Take LCM

$R = \frac{6-5}{6}$

$R = \frac{1}{6}$

Hence, the fraction of the paintings left with her is $\frac{1}{6}$