PSLE
Natalie had a total of 227 silver and black beads. She used 40 silver beads and 50% of the black beads. After that, the ratio of the number of silver beads to black beads Natalie had was 9 : 1.

1. What fraction of her black beads was Natalie left with? Give your answer in the simplest form.
2. How many more silver beads than black beads did Natalie have in the end?

	Silver	Black	Total
Before	9 u + 40	2 u	11 u + 40
Change	- 40	- 1 u
After	9 u	1 u	10 u
Comparing silver beads and black beads in the end	9	1	10

(a)
50% = ⁵⁰₁₀₀ = ¹₂

Fraction of her black beads that Natalie used = ¹₂

Fraction of her black beads that Natalie was left with
= 1 - ¹₂
= ¹₂

(b)
The number of black beads in the end is repeated.
Since the numbers are already the same, we do not need to use LCM to make them the same.

Number of black beads at first = 2 u
Number of silver beads at first = 9 u + 40

Total number of beads at first
= 2 u + 9 u + 40
= 11 u + 40

11 u + 40 = 227
11 u = 227 - 40
11 u = 187

1 u = 187 ÷ 11 = 17

Number of black beads in the end = 1 u
Number of silver beads in the end = 9 u

Number of more silver beads than black beads that Natalie had in the end
= 9 u - 1 u
= 8 u
= 8 x 17
= 136

Answer(s): (a)¹₂; (b) 136