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You can read the postings on **Sarin learns concept of ratio in school** and **Sarin learns the concept of Fraction (mathematics concept)** to understand the concept of Ratio and Fraction or Portion.

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

**Upper primary school mathematics question UPQ296**

Hairu had 42 more stickers than Fatimah. Each of them gave away some of their stickers to Sarin. The number of stickers Fatimah gave away was 4/7 of the number of stickers Hairu had at first. The number of stickers Hairu gave away was 2/3 of the number of stickers Fatimah had at first both had an equal number of stickers left. How many stickers did Hairu have at first?

Solution:

Using Math Model

Start with the different of stickers they had = 42

Subdivide Hairu to 7 equal blocks (7H) and Fatimah to 3 equal blocks (3F)

The give away from Fatimah was 4/7 fraction of Hairu = 4H of Hairu’s stickers

The give away from Hairu was 2/3 fraction of Fatimah = 2F of Fatimah’s stickers

Funally, they had same amount of stickers left

Redraw the model

From the model

2F = 4H + 42

1F = 2H + 21

Rearrange the model base interm of 1H

From the model

1H = 21 × 3 + 42 = 63 + 42 = 105

The number of stickers Hairu had at first = 7 × 105 = 735

Alternative solution:

By using Ratio,

Hairu had 42 stickers more than Fatimah at first

Ratio at first, Hairu : Fatimah = (1U + 42) : 1U

Hairu give away stickers = 4/7 fraction of Fatimah’s stickers

Fatimah give away stickers = 2/3 fraction of Hairu’s stickers

Final ratio, Hairu : Fatimah = (1U + 42 – 4/7 U) : 1U – 2/3( 1U + 42)

= (3U + 42 × 7)/7 : 1/3 U – 84/3

= (9U + 882) : (7U – 588)

The have same amount of stickers at the end

9U + 882 = 7U – 588

2U = 1470

1U = 735

The number of stickers hairu had at first is 735