2/5, 40%
Step-by-step explanation:
When we ask "six is what fraction of 15?", we're asking this: how much of 15 does 6 take up? Just looking at a picture of it, if we have 15 pieces of a whole cake, 6 of those pieces take up a little less than half of that total. We represent this with the fraction 6/15. Now, 6 and 15 have something in common, too: they can both be divided by 3. Take a look at the second picture now. Notice that when we divide the total number of parts and the number of pieces by the same number, the amount those pieces take up stays exactly the same. Since 6 divided by 3 is 2 and 15 divided by 3 is 5, we can say that 6/15 = 2/5, and we can't go any further than that.
Percents are just a special kind of fraction; ones that have 100 in their denominator (the word "percent" literally means "for each 100"). We also have a special way of writing percents: 6/100 would be written as 6%, 50/100 would be 50%, and 100/100 would be 100%.
Remember when I showed how fractions can be equal to each other if you can divide both number by the same thing? You can do the same thing in the other direction: you can create equivalent fractions by multiplying both numbers by the same number.
So, we want to go from 2/5 to ?/100 (we don't know what number ? is yet!) but how do we get there? Well, remember, for two fractions to be equal, you have to multiply both the top and bottom by the same number. Whatever we multiply 5 by to get 100, we'll have to multiply 2 by to get that ?
Well 5 × 20 = 100, so 20 seems to fit the bill, and multiplying 2 × 20 gets us 40, making our fraction 2/5 = 40/100, which we'd write as 40%.
So 6 is 2/5 of 15, which is the same as 40% of 15!
