# Math Help - Writing Fractions as Products

1. ## Writing Fractions as Products

In my book it merely lists the instructions "The steps you will follow are the same as multiplying fractions-only in reverse". I know that when you multiply fractions its "straight across", but this does not help me much I do not comprehend it and I cannot visualize it.

For instance $\frac{x+1}{2} = \frac{1}{2}(x+1)$

Another example is

$\frac{7x}{8}= \frac{7}{8}x$

Could some one please clarify in detail how I go about doing this exactly?

2. Originally Posted by allyourbass2212
In my book it merely lists the instructions "The steps you will follow are the same as multiplying fractions-only in reverse". I know that when you multiply fractions its "straight across", but this does not help me much I do not comprehend it and I cannot visualize it.

For instance $\frac{x+1}{2} = \frac{1}{2}(x+1)$

Another example is

$\frac{7x}{8}= \frac{7}{8}x$

Could some one please clarify in detail how I go about doing this exactly?

$\frac{x+1}{2} = (x+1) \div 2 = (x+1) \div \frac{2}{1} = (x+1) \times \frac{1}{2}$

Does this clarify it a bit for you?

3. There is no difference in saying: $\frac{ab}{c}$ and $\frac{a}{c} b$ or $\frac{b}{c}a$ or $\frac{1}{c} \times a \times b$

It's not a rule or anything. It's just that it doesn't matter whether you divide/multiply first.

For example, if you multiply: $\frac{4}{2} \times 5$

This is no different if you wrote it like this: $\frac{4 \times 5}{2}$ or $\frac{5}{2} \times 4$ or $\frac{1}{2} \times 5 \times 4$

You can divide 4 by 2 first and multiply by 5. Or you can multiply 4 and 5 first then divide by 2. Or you can divide 5 by 2 and then multiply by 4. Or you can multiply 1/2 and 5 and 4. They're all equivalent.