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When converting ratios to fractions which is the correct way of doing it? I've seen conflicting information that says the the denominator should be the total while other sources say the denominator can just be the second term.

For instance, if we have 3 apples, and 4 oranges, the ratio of apples to oranges can be written as:

$3:4$

When writing as a fraction, we can either write:

$\frac{3}{4}$

or

$\frac{3}{3+4}$ = $\frac{3}{7}$

Further when we convert this to a percent, I have seen this converted to either

$75\%$

which would mean there are 75% as many apples as oranges.

But it might also be written as

$43\%$

where the number of apples is 43% of the total items.

Are both fine as long as you are clear what you are trying to represent?

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  • $\begingroup$ Think of it this way: "there are $3$ Yes ballots in a box along with $4$ No Votes". Then the ratio of Yes to No is $3:4$ and $\frac 3{3+4}=\frac 37$ of the votes are Yes. $\endgroup$ – lulu Dec 13 '20 at 14:22
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    $\begingroup$ As long as you are clear about what you are trying to represent, yes. That is a very important thing to do. Both fractions are commonly used for various calculations and it is up to you to know which is useful for whatever situation you are in. As a mathematical object, "$3:4$" is just a ratio with no implied meaning or significance just like how "$5$" has no units. If I were told to go to the store to buy something that costs "$5$" I wouldn't know if that means I need to bring dollars, quarters, pennies, schotzkies, rupies, or otherwise. $\endgroup$ – JMoravitz Dec 13 '20 at 14:24
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    $\begingroup$ @JMoravitz made the important point, so I will not repeat his words. But think of this: There are $3$ apples and $4$ oranges, so there are $\frac{3}{4}=75\%$ as many apples as there are oranges. On the other hand, $\frac{3}{4+3}=\frac{3}{7}=42.857\ldots\%$ of all the fruits are apples. Both numbers are significant depending on what you want to do with them. $\endgroup$ – Luiz Cordeiro Dec 13 '20 at 14:28
  • $\begingroup$ Ok, I'm just seeing a lot of sites on the internet that always seem to convert $3:4$ as $\frac{3}{4}$ and don't even consider writing it as $\frac{3}{7}$, even though when dealing with fractions we almost are always referring to parts of the total. example $\endgroup$ – Kibbee Dec 13 '20 at 14:31
  • $\begingroup$ An example stating how $\frac{3}{7}$ would be the more correct way or writing it. $\endgroup$ – Kibbee Dec 13 '20 at 14:33
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Yes, as long as you know that $3/7$ is apples in a whole basket(lets say) and $3/4$ is relative, ie there are 3 apples for 4 oranges and that when you need to use which.

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