PSLE
A box contained black and silver beads. At first, the number of black beads was ¹₃ the number of silver beads. After ¹₂ of the black beads and ⁵₁₂ of the silver beads were used, 54 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?

	Black	Silver
Comparing black beads and silver beads at first	1x4 = 4 u	3x4 = 12 u
Before	2x2 = 4 u	12x1 = 12 u
Change	- 1x2 =  - 2 u	- 5x1 = - 5 u
After	1x2 =  2 u	7x1 = 7 u

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

The number of black beads at first is repeated.

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

Fraction of the beads used
= ^{2 + 5}_{4 + 12} 
= ⁷₁₆

(b)
Number of beads left
= 2 u + 7 u
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Number of beads at first
= 16 u
= 16 x 6
= 96

Answer(s): (a) ⁷₁₆; (b) 96