The blog postings are about the Singapore Math. The readers can learn from the postings on Solving Singapore Primary School Mathematics that teaches in Singapore Primary Schools. You or your kids can learn the skills of dealing with Math Modeling, Math Problem Solving, Problem Sum from Lower Primary School to Upper Primary School level after reading the blog postings. This posting is an upper primary school math question on Fraction, Ratio, and Problem Sum.

You can click here and read the posting on **A family in Singapore** about Sarin’s family.

Read also the posting on **Sarin learns concept of ratio in school **to understand the concept of Ratio.

Should read also the posting on **Sarin learns the concept of Fraction (mathematics concept)** to understand the concept of Fraction.

*Challenge yourself with the question before look for the given solution‼!*

**Upper primary school mathematics question UPQ285**

Sarin, Hairu and Fatimah received some money from their father. The ratio of the amount of money Sarin received to the amount of money Hairu received was 2 : 9. The ratio of the amount money Hairu received to the amount of money Fatimah received was 8: 5. Then, Hairu gave 1/12 of his money to Sarin, and Fatimah gave 1/9 of her money to Sarin. As a result, Sarin had $378 in the end.

(a) What was the ratio of the amount of money Sarin had to the amount of money Hairu had in the end? (Give your answer in its simplest form.)

(b) What was the total amount of money that three of them has?

Solution:

Start with the money ratio at first

Sarin : Hairu = S : H = 2 : 9 = 16 : 72

Hairu : Fatimah = H : F = 8 : 5 = 72 : 45

Sarin : Hairu: Fatimah = S : H : F = 16 : 72 : 45

The total amount of money did no change and the money is shifting among them

After Hairu gives 1/12 of his money to Sarin

S : H : F = (16 + 72/12) : (72 – 72/12) : 45 = 22 : 66 : 45

After Fatimah gives 1/9 of her money to Sarin

S : H : F = (22 + 45/9) : 66 : (45 – 45/9) = 27 : 66 : 40

The final ration of Sarin to Hairu = S : H = 27 : 60 = 9 : 22

Sarin finally had in term of units = 27

27 units = 378

1 unit = $14

Total amount of the three of them = 133 × 14 = $1862

Alternative Solution:

By math model

Draw base on ratio of money at first

In the end, the amount of money no change but shifted among them

1/12 fraction of Hairu given to Sarin = 72/12 = 6 units

1/9 fraction of Fatimah given to Sarin = 45/9 = 5 units

Per the model,

The final ratio of Sarin to Hairu = 27 : 66 = 9 : 22

27 units = 378

1 unit = $14

The total amount three of them had = 133 × 14 = $1862