Work out \(\frac{3}{5}\div\frac{9}{10}\). Give your answer as a fraction in its simplest form.
Question 1 Report
Work out \(\frac{3}{5}\div\frac{9}{10}\).
Give your answer as a fraction in its simplest form.
Answer Details
Dividing by a fraction is the same as multiplying by its reciprocal, because dividing by \(\frac{9}{10}\) asks how many lots of \(\frac{9}{10}\) fit into the first number.
\[ \frac{3}{5}\div\frac{9}{10} = \frac{3}{5}\times\frac{10}{9} \] [M1]Cancel before multiplying: \(3\) and \(9\) share a factor of \(3\), and \(5\) and \(10\) share a factor of \(5\).
\[ \frac{3}{5}\times\frac{10}{9} = \frac{1}{1}\times\frac{2}{3} = \frac{2}{3} \]The answer is \(\frac{2}{3}\) [A1]
The result is less than \(1\) because \(\frac{3}{5}\) is smaller than \(\frac{9}{10}\), so it does not contain a whole copy of it. A common error is to invert the first fraction instead of the second; only the divisor is turned upside down.
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