Some Thoughts

Fractions : Maths vs English

1 April 2021

I really enjoy maths and my son seems to have picked up this trait, one of the things we’ve enjoyed together is learning about fractions.

It’s one of those things that lots of people find really confusing and I’ve been trying to understand that.

Maths is a Language

I like this TED talk a lot: Math isn’t hard, it’s a language

I think it captures a lot of the problems and opportunities in how we talk about maths

Adding Fractions

The main example given is that one apple plus one apple is two apples.

one million plus one million is two million

and one third plus one third is two thirds

Because the rule is one plus one equals two

and as long as we are adding the same kind of thing it doesn’t matter if that thing is million, apple, or third.

1/3 + 1/3 = 2/3

You don’t need to know about numerators and denominators to do that.

In maths it can help to know the words for things - just like in English you don’t always need to know the names of grammar rules to be able to use them - but it can be helpful.

Maths is a Different Language

This shows up when we talk about multiplying and dividing fractions

You can say things in maths that don’t make sense in English.

Dividing by Fractions

5 ÷ 1/2 = 10

Five divided by a half equals ten.

In maths that works - but in English it’s nonsense.

This is partly because in English it doesn’t make much sense to talk about pure numbers - we normally talk about numbers of a thing.

But we can find a way to say it that does make sense.

Five apples chopped in half gives ten pieces.

Multiplying by Fractions

10 × 1/2 = 5

This isn’t quite as odd but still not quite normal English

Ten half portions are the same as 5 portions.


Ten lots of half an apple is the same as 5 apples.

How to Get Used to Maths

  • find concrete examples to express the concept
  • don’t expect the maths sentence to make sense directly in English
  • don’t panic if it doesn’t make intuitive sense right away : practise

I know that often when I have been learning maths I have had the uncomfortable feeling at first that I don’t understand it.

But once I’ve practised, learned the rules, and gotten used to it, the feeling of not understanding goes away.