PSLE
A box contained green and red beads. At first, the number of green beads was ¹₃ the number of red beads. After ¹₂ of the green beads and ¹₄ of the red beads were used, 66 beads were left.

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

	Green	Red
Comparing green beads and red 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 red beads at first is repeated. Make the number of red beads at first the same. 
LCM of 3 and 4 is 12.

The number of green beads at first is repeated.

Since the number of green beads at first is 4 u, we make the total number of green 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 = 66

1 u = 66 ÷ 11 = 6

Number of beads used
= 2 u + 3 u
= 5 u
= 5 x 6
= 30

Answer(s): (a) ¹¹₁₆; (b) 30