PSLE
At first, Penelope had an equal number of green and purple marbles . She gave away ²₃ of her green marbles and some purple marbles. In the end, she was left with ¹₄ of her marbles. What fraction of the purple marbles did Penelope give away?

	Green	Purple	Total
Comparing green marbles and purple marbles at first	1x3x2 = 6 u	1x3x2 =  6 u	2x3x2 =  12 u
Before	3x2 = 6 u	6 u	4x3 = 12 u
Change	- 2x2 = - 4 u	- 5 u	- 1x3 = - 9 u
After	1x2 = 2 u	1 u	3x3 = 3 u

After1_x2 =
2 u
1 u3_x3 =
3 u
The number of green marbles at first is repeated. Make the number of green marbles the first the same. LCM of 3 and 1 is 3.

The total number of marbles at first is repeated. Make the total number of marbles at first the same. LCM of 6 and 4 is 12.

Number of purple marbles that Penelope was left with
= 3 u - 2 u
= 1 u

Number of purple marbles that Penelope gave away
= 6 u - 1 u
= 5 u

Fraction of the purple marbles that Penelope gave away = ⁵₆

Answer(s): ⁵₆