PSLE
A box contained orange and gold beads. At first, the number of orange beads was ¹₅ the number of gold beads. After ¹₃ of the orange beads and ⁸₉ of the gold beads were used, 132 beads were left.

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

	Orange	Gold
Comparing orange beads and gold beads at first	1x9 = 9 u	5x9 = 45 u
Before	3x3 = 9 u	9x5 = 45 u
Change	- 1x3 =  - 3 u	- 8x5 = - 40 u
After	2x3 =  6 u	1x5 = 5 u

(a)
The number of gold beads at first is repeated. Make the number of gold beads at first the same. 
LCM of 5 and 9 is 45.

The number of orange beads at first is repeated.

Since the number of orange beads at first is 9 u, we make the total number of orange beads at first the same by multiplying 3 by 3 to become 9 u too.

Fraction of the beads left
= ^{6 + 5}_{9 + 45} 
= ¹¹₅₄

(b)
Number of beads left
= 6 u + 5 u
= 11 u

11 u = 132

1 u = 132 ÷ 11 = 12

Number of beads used
= 3 u + 40 u
= 43 u
= 43 x 12
= 516

Answer(s): (a) ¹¹₅₄; (b) 516