Originally Posted by

**lamp23** I agree defining division first feels more natural and think it may be because you might not be able to draw a picture of a fraction without having divided something into equal groups/pieces.

The motivation for fractions could be for measurements, but I'm trying to think if there's a need for multiplication of fractions or it's just a convenience. For instance $\displaystyle 1 inch = 1/12 foot = 1/12 \cdot 1/3 yard$ but we could have stated:

$\displaystyle 1 foot \div 12 = 1 yard \div 3 \div 12$