Why do children (and adults) find fractions so complicated…?
My own children seem to fear them and I don’t really understand why. They were introduced to fractions as soon as they started eating sandwiches. So why do they claim they don’t understand them?
Eating sandwiches? Yes, “shall I cut them in half for two pieces or quarters for four?” To me this seemed an obvious introduction (although of course the cutting did not always lead to equally sized pieces!) In the same way we talk about the time quarter to, quarter past and half past the hour. So why is there suddenly that cry of “I hate fractions?” I do think that a lot of people fear fractions because they don’t really understand what the numerator and denominator actually represent. Pupils gleefully call out the words to me, they are known facts – but I think the focus has been on the language behind the fraction and not necessary understanding what the language represents.
So what is a denominator? We have common denominators? But what does it all mean?
The denominator is the bottom number on the fraction. Yes, we all know that, that is what we have been taught but I do think children were so caught up in learning the word they missed the important bit.
The denominator describes how many parts a whole amount has been split into. So if we talk about thirds (talk and not write) we are splitting a whole into three equal parts. Tenths would be ten equal parts, fifths would be five and so on. I think that this is the key to really understanding fractions. The denominator describes how many parts a whole amount has been split into.
Now to the numerator – well it’s the top number of course! But, what does that mean?
If you were to eat three quarters of a pizza how many slices would you have and how many have you eaten? So the denominator (the bottom number) tells us we had four pieces (quarter – and yes fourths seem acceptable now) and the three (the numerator or top number) tells us how many of the four pieces we ate. The numerator describes how many parts of the whole we have.
four fifths – means a whole amount has been split into 5 equally sized parts and we have 4 of these parts
seven tenths – means a whole amount has been split into 10 equally sized parts and we have 7 of these parts
A few other fractions facts to think about:
- fractions, decimals and percentages are different ways of representing parts of whole number
- a fraction represents a division – the numerator divided by the denominator will create a decimal
- multiply the decimal by 100 and you have the percentage
- the line that separates the numerator and denominator is called a vinculum (maybe an interesting fact for a pub quiz!)
Which leads me to pizza and chocolate…