PSLE
A box contained purple and black beads. At first, the number of purple beads was ¹₅ the number of black beads. After ¹₃ of the purple beads and ²₉ of the black beads were used, 410 beads were left.

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

	Purple	Black
Comparing purple beads and black beads at first	1x9 = 9 u	5x9 = 45 u
Before	3x3 = 9 u	9x5 = 45 u
Change	- 1x3 =  - 3 u	- 2x5 = - 10 u
After	2x3 =  6 u	7x5 = 35 u

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

The number of purple beads at first is repeated.

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

Fraction of the beads left
= ^{6 + 35}_{9 + 45} 
= ⁴¹₅₄

(b)
Number of beads left
= 6 u + 35 u
= 41 u

41 u = 410

1 u = 410 ÷ 41 = 10

Number of beads used
= 3 u + 10 u
= 13 u
= 13 x 10
= 130

Answer(s): (a) ⁴¹₅₄; (b) 130