Sharing between three

What Is a Third?

Thirds are the first fraction that refuses to divide neatly. That is what makes them interesting.

Harder to cut than halves, and harder to write down.

Step 1 of 5

Three friends, one pizza.

A third never lands on a tidy decimal — 0.333… runs on forever.

Everyone gets the same amount, so the pizza is cut into three matching pieces. Each person has one third.
Step 2 of 5

Thirds are harder to cut than halves.

No fold lands on a third, which is why hand-cut thirds are always a bit wrong.

You can halve by folding. Cutting three equal pieces by eye is genuinely difficult, which is why third-cuts are usually a bit wrong.
Step 3 of 5

Three thirds make a whole.

Put all three pieces back and the pizza is complete. Two thirds is two of those pieces — most of it, but not all.
Step 4 of 5

A third is bigger than a quarter.

Cutting into fewer pieces makes each piece bigger. The bigger the bottom number, the smaller each share.
Step 5 of 5

As a decimal it never ends.

One third is 0.3333… forever. Ten does not divide by three evenly, so the decimal repeats endlessly. The fraction 1/3 is the exact version.

Add 0.333… three times and you get 0.999… — which really does equal 1, and mathematicians have proved it.

The short version

A third is one of three equal shares — bigger than a quarter, and impossible to write exactly as a decimal.

Try cutting a strip of paper into three equal pieces by eye, then measure. Almost nobody gets it right first time.