## x to the minus 1 = 1 over x. OK?

I have posted before about the difficulties that students have with fractions and the problems that this causes. Many others recognise the same difficulty.

On a related point, students also have problems with reciprocation, and sometimes it is simply that they don’t recall that x^{-2}=1/x^{2}

So the analysis of the question shown on the right should not be too surprising. The question is very well answered, but the ‘correct’ option that students are least likely to select is the one shown highlighted (top right). This is present in about 86% of all answers, but all the other correct options are present in more than 90% of answers.

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