A farmer waters part of a field's irrigation channel each morning before the sun gets too hot. \(\frac{3}{8}\) of the channel is opened, and \(\frac{4}{9}\)...
Question 1 Report
A farmer waters part of a field's irrigation channel each morning before the sun gets too hot. \(\frac{3}{8}\) of the channel is opened, and \(\frac{4}{9}\) of that opened section feeds young crops nearest the gate. Work out the fraction of the whole channel that feeds young crops, giving your answer in its simplest form. (2)
Answer Details
This question tests multiplying fractions to find "a fraction of a fraction" of the whole channel. Since \(\frac{4}{9}\) of the opened \(\frac{3}{8}\) of the channel feeds young crops, the fraction of the whole channel is \(\frac{3}{8} \times \frac{4}{9} = \frac{3 \times 4}{8 \times 9} = \frac{12}{72}\) [1 mark].
Simplifying by dividing the numerator and denominator by their highest common factor, 12, gives \(\frac{12}{72} = \frac{1}{6}\) [1 mark]. So one sixth of the whole channel feeds the young crops nearest the gate.
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