If you choose to divide fractions using the standard technique of multiplying by the reciprocal, how could you use cell 2 and cell 4 as a learning experience? i.e. Would you provide these as something that higher attaining students can verify with more examples? When might it be easier to use cell 4 rather than multiplying by the reciprocal?

In regards to cell 2, would you ever consider teaching fractions by always finding a common denominator first when adding, subtracting, multiplying and dividing – then have students reflect on which operation they don’t need to do this for?