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
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.
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
A bar is cut into $4$ equal pieces. What is one piece called?
How many quarters make one whole?
A cake is cut into $4$ pieces, some bigger than others. Otim says each piece is a quarter. Is he right?
What is $\frac{1}{3}$ of $24$?
A bar is cut into $5$ equal pieces. What is one piece called?
What is $\frac{1}{8}$ of $40$?
Away from the screen
Show that you have it
Equal, or not a fraction at all
A cake is cut into $3$ pieces, some bigger than others. Otim says each piece is a third. Is he right?
What is $\frac{1}{12}$ of $84$?