dividing by fractions

[brucestl]

How do you explain to a young person that when you divide by a fraction you come out with a larger number or fraction?

 

[soroban]

Hello, brucestl!

How do you explain to a young person that when you divide by a fraction,
you come out with a larger number or fraction?

We have a 6-foot board.

We cut it into 2-foot pieces. .How many pieces do we have?
. . $\displaystyle 6 \div 2 \:=\:3$ pieces.

We cut it into 1-foot pieces. .How many pieces do we have?
. . $\displaystyle 6 \div 1 \:=\:1$ pieces.

We cut it into $\displaystyle \frac{1}{2}$-foot pieces. .How many pieces do we have?
. . $\displaystyle 6 \div \frac{1}{2} \:=\:12$ pieces.

We cut it into $\displaystyle \frac{1}{4}$-foot pieces. .How many pieces do we have?
. . $\displaystyle 6\div\frac{1}{4} \:=\:24$ pieces.


Hence, the smaller the pieces, the more pieces we have.