PSLE
A box contained yellow and gold beads. At first, the number of yellow beads was ¹₃ the number of gold beads. After ¹₄ of the yellow beads and ⁷₈ of the gold beads were used, 54 beads were left.

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

	Yellow	Gold
Comparing yellow beads and gold beads at first	1x8 = 8 u	3x8 = 24 u
Before	4x2 = 8 u	8x3 = 24 u
Change	- 1x2 =  - 2 u	- 7x3 = - 21 u
After	3x2 =  6 u	1x3 = 3 u

(a)
The number of gold beads at first is repeated. Make the number of gold beads at first the same. 
LCM of 3 and 8 is 24.

The number of yellow beads at first is repeated.

Since the number of yellow beads at first is 8 u, we make the total number of yellow beads at first the same by multiplying 4 by 2 to become 8 u too.

Fraction of the beads left
= ^{6 + 3}_{8 + 24} 
= ⁹₃₂

(b)
Number of beads left
= 6 u + 3 u
= 9 u

9 u = 54

1 u = 54 ÷ 9 = 6

Number of beads used
= 2 u + 21 u
= 23 u
= 23 x 6
= 138

Answer(s): (a) ⁹₃₂; (b) 138