The question is self-explanatory, but I'll give a specific example that will help me understand this.
I did a word problem recently that I need help with, but I'll skip to the part that I'm puzzled over.
Ignore the k times 52 and go to the 5 halves times 52. I understand everything up to this point. What I want to know is, how does 5 halves times 52 become 5 times 26? What I thought you would do was multiply the 2 on both sides to get rid of the fraction and end up with 5 times 104? How did they get 5 times 26?
Thank you for your response in advance.
Did you know this? $$\frac 5 2 = \frac 1 2 \times 5$$
In fact, it is generally true that $$ \frac a b \times c = \frac 1 b \times a \times c = \frac {a\times c} b$$
The most important thing to know here is that writing something like $\frac 5 2$ is shorthand. What's really going on when you write $\frac 5 2$ is that you write $\frac 1 2 \times 5$. The fraction $\frac 1 2$ is just a number, and all that's going on here is multiplication.
We create fractions as multiplicative inverses: for example, the number $\frac 1 3$ is defined as the number $x$ such that $ x \times 3 =1$. The fraction $\frac 1 2$ is the number $x$ such that $x \times 2 = 1$. The fraction $\frac 1 {502}$ is the number $x$ such that $x \times 502 = 1$. For every positive integer ($1,2,3,4,\ldots$) there is a corresponding number such that those two numbers, when multiplied, yield $1$.
So it's useful to think about this as $\frac 5 2$ as being equivalent to $5 \times \frac 1 2$. And that goes both ways: $\frac 1 2 \times 5$ is $\frac {5\times 1} 2$. And $\frac 5 2 \times 2$ is $\frac {5 \times 2} 2$.
Referring back to the original problem and the rule I mentioned at the start, we now see:
$$\frac 5 2 \times 52 = \frac {5 \times 52} 2 = \frac {52} {2} \times 5$$
And you know that $\frac {52} {2} = 26$, so:
$$\frac {52} 2 \times 5 = 26 \times 5 = 130$$