⁦Complex fractions⁩

⁦A fraction whose top or bottom is a fraction⁩: ⁦share a fraction on a bar, count fractions inside fractions, and divide by flipping the lower fraction⁩.

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الدليل

A كسر بسطه ومقامه كسران ⁦has a fraction in its numerator or its denominator, for example ١٢٢ or ٢٣١٦⁩. ⁦The long fraction bar means divide⁩: ⁦the top is divided by the bottom⁩.

⁦١٢٢ is half of a half⁩. ⁦On a bar, take the striped half and share it between 2⁩: ⁦one share is one quarter of the whole bar⁩. ⁦So ١٢٢ = ١٤⁩.

⁦When the bottom is a fraction, flip it and multiply⁩: ⁦٢٣٤٥ = ٢٣ × ٥٤⁩. ⁦Dividing by ١٦ asks⁩ "⁦how many sixths fit in it⁩?", ⁦which is the same as multiplying by 6⁩.