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Upper primary school mathematics question UPQ134

1/3 of Fatimah’s marbles is 20 more than ¼ of Hairu’s marbles. If Fatimah gives half of his marbles to Hairu, Hairu will have 64 more marbles than Fatimah.

(a) How many marbles does Fatimah have?

(b) What fraction of Fatimah’s marbles is Hairu’s marbles? Leave your answer in the simplest form.

* *Solution:

Draw the model as shown:

From the model

8 units = 64

1 unit = 8

The number of marbles that Fatimah had = 6 × 8 + 3 × 20 = 108

The number of marbles that Hairu has = 8 × 8 = 64

The fraction of Fatimah’s marbles to Hairu’s marbles = 108/64 = 27/16 = 1 11/16

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