What Is a Fraction?

What a fraction is

A fraction is a number that describes part of a whole.

Cut a chocolate bar into four equal pieces, take three of them, and you are holding an amount that no whole number describes. It is plainly more than nothing and just as plainly less than a bar, and until fractions arrive a child has no way of writing it down. That is the gap fractions were invented to fill.

We write that as 34 and say it "three quarters".

The two numbers

Every fraction carries two numbers, and they are doing completely different jobs. Unfortunately they were given long names that sound almost the same, so children mix them up for years, usually without ever being told there is a way to keep them straight.

Why the parts have to be equal

Ask a class to shade three quarters of a rectangle and you will get three different answers, and only one of them is really about fractions. The other two are about drawing. This is the idea that gets rushed past, and it is the one everything else rests on.

Snap a chocolate bar into four pieces where one of them is obviously bigger than the rest, and none of those pieces is a quarter. Not the big one, and not the small ones either. A quarter is not one of four pieces, it is one of four equal pieces, and dropping that single word turns a fraction into a guess.

Try it at home with a sheet of paper. Tear it roughly into four uneven bits, hold one up, and ask whether it is a quarter. A child who has understood will say no straight away and tell you why. A child who has only learned the words will say yes, and now you know exactly what to work on.

Fractions on a number line

Shaded shapes are where fractions start, and for a lot of children they are also where fractions stop. That becomes a problem later, because a fraction is a number, and every question about comparing or ordering assumes the child can put it somewhere on a line. Introducing the line early costs nothing and saves a great deal of confusion in Grade 5.

Look where 44 lands. Four quarters take you to exactly 1, because four quarters are the whole thing, and a child who sees that on the line will accept it far more readily than one who is told it.

Reading fractions aloud

The names run to a pattern once you are past the first few, and the first few are the awkward ones.

• 12 is a half, not a "onerth".
• 13 is a third.
• 14 is a quarter, and some books say "fourth".
• From five onwards it is regular: 15 a fifth, 16 a sixth, 110 a tenth.
• Change the top number and the name just gets a count in front: 35 is three fifths.

Common mistakes

Practice questions

Seven questions. One attempt each, and the explanation appears once the answer is in.

What to learn next