PSLE
A box contained black and yellow beads. At first, the number of black beads was ¹₃ the number of yellow beads. After ¹₂ of the black beads and ³₄ of the yellow beads were used, 20 beads were left.

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

	Black	Yellow
Comparing black beads and yellow beads at first	1x4 = 4 u	3x4 = 12 u
Before	2x2 = 4 u	4x3 = 12 u
Change	- 1x2 =  - 2 u	- 3x3 = - 9 u
After	1x2 =  2 u	1x3 = 3 u

(a)
The number of yellow beads at first is repeated. Make the number of yellow beads at first the same. 
LCM of 3 and 4 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 left
= ^{2 + 3}_{4 + 12} 
= ⁵₁₆

(b)
Number of beads left
= 2 u + 3 u
= 5 u

5 u = 20

1 u = 20 ÷ 5 = 4

Number of beads used
= 2 u + 9 u
= 11 u
= 11 x 4
= 44

Answer(s): (a) ⁵₁₆; (b) 44