Confusion with percentages.

percent is *per cent*, or “per 100”.

When you divide one number by another and get a decimal, you’re getting how much out of 1 that number is. Such as 13/20=0.65/1. Multiply top and bottom by 100 and you get 65/100, or 65 per 100; 65%.

Another way to think about it is that 1 is a whole. When you divide 13 by 20, you’re saying that 20 parts makes up one whole. So whatever your decimal is, that’s how much of one whole you have. Similarly, you multiply by 100 (top and bottom) to get what that part of the whole would be when one whole is 100 parts.
You are using proportional thinking.

Easy case:

13/20 = x/100

You noticed that 5 works to change 20 to 100 in denominator, so you multiply by 5/5 to write 13/20 as an equivalent fraction.

13/20 * 5/5 = 65/100

So percent is 65%.

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Harder case:

5.05/28 = x/100

You seek something that will turn 28 to 100 by multiplication. It's 100/28, because 28 * 100/28 = 100. So this time you multiply by (100/28)/(100/28).

5.05/28 * (100/28)/(100/28) = x/100

Now simplify and compare numerators.

5.05 * 100/28 = x

Your trick does the same thing.

5.05 / 28 * 100 = x

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You don't have to use equivalent fractions approach. You might use an equation solving strategy of multiplying each side by 100:

5.05/28 = x/100

5.05/28 * 100 = x/100 * 100

5.05 / 28 * 100 = x
What you are doing is

5.05/28=x/100

x=5.05×100/28=

5.05/28×100=18.0%
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