Pizza or Chocolate – the best way to compare fractions

For many years I taught fractions with pizzas and cakes, then one day I realised I had been doing it all wrong…

Cakes and pizzas seem to lend themselves nicely to fractions but not when you’re trying to compare fractions. Many meal times often almost end in disaster at our house and this is because a circular cake is brought to the table and one of the children attempt to cut into equally sized pieces.

Where is the centre of the cake? Are we sure they the sixths are really sixths, what fraction should we start with to make the sixths…in fact I am sure someone should have invented a cake cutting protractor by now..?! (maybe you’ll see me on Dragon’s Den soon!)

So, I’m going to start making rectangular cakes from now or just have bars of chocolate

And this is why…

Consider the question which is greater 2/3 or 3/5? I am sure you can visualise this but how do you really justify your answer…


So the circles seem to make sense at first glance but grab yourself a piece of paper and draw them. Do they make sense now? Can you be certain which fraction is bigger? So I prefer rectangles or chocolate bars. They are much easier to draw and easier to overlay.

From my previous blog we know that 2/3, is a whole amount split into 3 equal parts and we are considering 2 of them. So we draw a rectangle, split horizontally into 3 equal pieces and shade 2 of them.


Next the 3/5, so this is a whole amount split into 5 equal parts and we need 3 of them. Again we draw another rectangle and this time split vertically into 5 equally sized pieces and shade 3.


But, you’re still none the wiser…how do these compare easily. So now imagine the two rectangles sliding over each other and you will now have 15 small squares in each diagram.


You should now be able to see from your original diagram that 2/3 is now 10 of the smaller squares and 3/5 is 9 of the smaller squares and so 2/3 is greater than 3/5

And this is why I now prefer chocolate!

Can I add at this point, your children may not have been taught this at school in this manner and so I would like to scream “IT DOESN’T MATTER” if you now understand how to compare fractions, you are able to teach this to your child and you will all benefit!  

By the way, can you now see where the common denominator comes from?



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