One of the equal parts

Before you read anything

Tear a strip of paper into four pieces. Do not measure — just tear.

Now hold up one piece and ask yourself, honestly, whether it is a quarter.

The word everybody drops

Four equal pieces, and one of them is a quarter. Four uneven pieces, and not one of them is.

Both bars are cut into four. Only one of them has quarters in it.

What the bottom number says

:x nutshell-unit-fraction

One of however many equal parts. The bottom number says how many the whole was cut into, and therefore how big one piece is.

Cut a bar into five and one piece is a fifth. Cut it into twelve and one piece is a twelfth — smaller, because there are more of them. The bottom number is a :size, and it is the only job it has.

You have done the cutting already

$\frac{1}{4}$ of $20$ is $5$. That is twenty shared between four, which is module 6 — finding a unit fraction of something is dividing, and you have been doing it since before it had this notation.

Musa

said a twelfth must be bigger than a fifth because 12 > 5

More pieces means smaller pieces. Twelve of them have to fit in the same bar that five had to fit in.

Check yourself

Six to try

Say each one out loud in words first. Two of these are about whether the pieces are equal, and those are the ones that matter most.

1

A bar is cut into $4$ equal pieces. What is one piece called?

2

How many quarters make one whole?

3

A cake is cut into $4$ pieces, some bigger than others. Otim says each piece is a quarter. Is he right?

4

What is $\frac{1}{3}$ of $24$?

5

A bar is cut into $5$ equal pieces. What is one piece called?

6

What is $\frac{1}{8}$ of $40$?

One of the equal parts · page 1 of 2 Print it

One of the equal parts · page 2 of 2 Print it

Show that you have it

Equal, or not a fraction at all

The first asks whether four pieces are really quarters. The second is a division wearing fraction notation.

1

A cake is cut into $3$ pieces, some bigger than others. Otim says each piece is a third. Is he right?

2

What is $\frac{1}{12}$ of $84$?

Next: More than one slice The whole thing on one page