For all numbers $a$, $b$, and $c$,
I recommend you to question all your beliefs, except that two and two make four. As quoted in
The Number Sense (2011)
For every number $a$,
The number $A$ is often called the reciprocal of $a$ and is denoted by $1/a$.
I suppose $6/3$ better equal $2$.
How about something like $\frac{1}{2}\times \frac{1}{3}$?
I guess it oughtta be $1/6$, since
Now let's try $\frac{5}{2}\times \frac{4}{3}$.
When you multiply/divide a long string of numbers, you can move things around via commutativity and associativity, as long as you express the division in terms of multiplication.
Addition and subtraction have a similar relationship. Thus, to understand how subtraction works with respect to the properties, it helps to think in terms of addition of negative numbers.
How do we add fractions with common denominators? Something like:
$$\frac{2}{7} + \frac{4}{7} = ?$$I guess we add the numerators and put the result over the same denomominator.
I wonder why that works, though?
We're wondering if:
$$\frac{a}{b} + \frac{c}{b} = \frac{a+b}{b}?$$If the denominators aren't the same, we can always multiply top and bottom by the appropriate things to make them the same.
Conventionally, $5\frac{1}{2}$ means $5+\frac{1}{2}$.
Thus, if we want to multiply this kind of number by another, we can use the distributive property.