PSLE
A box contained yellow and orange beads. At first, the number of yellow beads was ¹₃ the number of orange beads. After ¹₄ of the yellow beads and ⁷₈ of the orange beads were used, 81 beads were left.

1. What fraction of the beads were used? Leave your answer in the simplest form.
2. How many beads were there in the box at first?

	Yellow	Orange
Comparing yellow beads and orange 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 orange beads at first is repeated. Make the number of orange 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 used
= ^{2 + 21}_{8 + 24} 
= ²³₃₂

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

9 u = 81

1 u = 81 ÷ 9 = 9

Number of beads at first
= 32 u
= 32 x 9
= 288

Answer(s): (a) ²³₃₂; (b) 288