PSLE
A box contained yellow and black beads. At first, the number of yellow beads was ¹₃ the number of black beads. After ³₄ of the yellow beads and ⁷₈ of the black beads were used, 35 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	Black
Comparing yellow beads and black beads at first	1x8 = 8 u	3x8 = 24 u
Before	4x2 = 8 u	8x3 = 24 u
Change	- 3x2 =  - 6 u	- 7x3 = - 21 u
After	1x2 =  2 u	1x3 = 3 u

(a)
The number of black beads at first is repeated. Make the number of black 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
= ^{2 + 3}_{8 + 24} 
= ⁵₃₂

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

5 u = 35

1 u = 35 ÷ 5 = 7

Number of beads used
= 6 u + 21 u
= 27 u
= 27 x 7
= 189

Answer(s): (a) ⁵₃₂; (b) 189