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Sharing between three

What Is a Third?

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

1One whole2 Cut into threeequal pieces33Take one — athird
Harder to cut than halves, and harder to write down.

  1. Step 1 of 5

    Three friends, one pizza.

    Three equal shares

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

  2. Step 2 of 5

    Thirds are harder to cut than halves.

    Halving Fold and it is exactThirding No fold does it — youmust judge

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

  3. Step 3 of 5

    Three thirds make a whole.

    Three thirdsthe whole thingTwo thirds2/3One third1/3

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

  4. Step 4 of 5

    A third is bigger than a quarter.

    One third Cut into 3 — biggerpieceOne quarter Cut into 4 — smallerpiece

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

  5. Step 5 of 5

    As a decimal it never ends.

    As a fraction 1/3 — exactAs a decimal 0.333… — never finishes

    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 it yourself

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

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