PSLE
A box contained blue and red beads. At first, the number of blue beads was ¹₃ the number of red beads. After ¹₂ of the blue beads and ¹₁₂ of the red beads were used, 156 beads were left.

1. What fraction of the beads were used? Leave your answer in the simplest form.
2. How many beads were there in the box at first?

	Blue	Red
Comparing blue beads and red beads at first	1x4 = 4 u	3x4 = 12 u
Before	2x2 = 4 u	12x1 = 12 u
Change	- 1x2 =  - 2 u	- 1x1 = - 1 u
After	1x2 =  2 u	11x1 = 11 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 12 is 12.

The number of blue beads at first is repeated.

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

Fraction of the beads used
= ^{2 + 1}_{4 + 12} 
= ³₁₆

(b)
Number of beads left
= 2 u + 11 u
= 13 u

13 u = 156

1 u = 156 ÷ 13 = 12

Number of beads at first
= 16 u
= 16 x 12
= 192

Answer(s): (a) ³₁₆; (b) 192