PSLE
A box contained purple and orange beads. At first, the number of purple beads was ¹₃ the number of orange beads. After ¹₂ of the purple beads and ¹₄ of the orange beads were used, 110 beads were left.

1. What fraction of the beads were left? Leave your answer in the simplest form.
2. How many beads were used?

	Purple	Orange
Comparing purple beads and orange beads at first	1x4 = 4 u	3x4 = 12 u
Before	2x2 = 4 u	4x3 = 12 u
Change	- 1x2 =  - 2 u	- 1x3 = - 3 u
After	1x2 =  2 u	3x3 = 9 u

(a)
The number of orange beads at first is repeated. Make the number of orange beads at first the same. 
LCM of 3 and 4 is 12.

The number of purple beads at first is repeated.

Since the number of purple beads at first is 4 u, we make the total number of purple beads at first the same by multiplying 2 by 2 to become 4 u too.

Fraction of the beads left
= ^{2 + 9}_{4 + 12} 
= ¹¹₁₆

(b)
Number of beads left
= 2 u + 9 u
= 11 u

11 u = 110

1 u = 110 ÷ 11 = 10

Number of beads used
= 2 u + 3 u
= 5 u
= 5 x 10
= 50

Answer(s): (a) ¹¹₁₆; (b) 50