The working for the example at the bottom of the left hand page is as follows:
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Paul demonstrates here his ability to recognise and factor the difference of two squares. |
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He knows how to multiply two fractions together by multiplying the two numerators and the two denominators. |
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In this final step he has recognised two equal factors that can be cancelled and has proceeded to cancel them. His Maths Teacher would have preferred that he mark the cancelling in the previous step by a line through each factor. |
At the next harder example he is not so successful. This is the example at the top of the right hand page:
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Paul is completely lost with this example. It is a bit of a mystery how he managed to produce the result he got. His concentration had certainly lapsed when he copied an addition sign instead of the multiplication sign! |
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This was the correction made by his teacher. It is somewhat brief and the details of the cancelling are not shown . Would Paul have understood this step? |
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We should give Paul credit where credit is due. This is his subsequent working from his mistake and is a perfectly correct step. Paul shows an ability to add two fairly complicated algebraic fractions. |
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