Hairu shares his stickers part 34 (Math Question)

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

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  

More Questions on Problem Sum. Click here….

More Questions on Fraction and Ratio. Click here….

 

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